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Journal articles on the topic 'Bayesian estimators'

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Published: 4 June 2021

Last updated: 17 June 2025

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Hu, Xue, and Haiping Ren. "Statistical inference of the stress-strength reliability for inverse Weibull distribution under an adaptive progressive type-Ⅱ censored sample." AIMS Mathematics 8, no. 12 (2023): 28465–87. http://dx.doi.org/10.3934/math.20231457.

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<abstract>In this paper, we investigate classical and Bayesian estimation of stress-strength reliability $\delta = P(X &gt; Y)$ under an adaptive progressive type-Ⅱ censored sample. Assume that $X$ and $Y$ are independent random variables that follow inverse Weibull distribution with the same shape but different scale parameters. In classical estimation, the maximum likelihood estimator and asymptotic confidence interval are deduced. An approximate maximum likelihood estimator approach is used to obtain the explicit form. In Bayesian estimation, the Bayesian estimators are derived based on symmetric entropy loss function and LINEX loss function. Due to the complexity of integrals, we proposed Lindley's approximation to get the approximate Bayesian estimates. To compare the different estimators, we performed Monte Carlo simulations. Under gamma prior, the approximate maximum likelihood estimator performs better than Bayesian estimators. Under non-informative prior, the approximate maximum likelihood estimator has the same behavior as Bayesian estimators. In the end, two data sets are used to prove the effectiveness of the proposed methods.</abstract>

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Neath, Andrew A., and Natalie Langenfeld. "A Note on the Comparison of the Bayesian and Frequentist Approaches to Estimation." Advances in Decision Sciences 2012 (October 22, 2012): 1–12. http://dx.doi.org/10.1155/2012/764254.

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Samaniego and Reneau presented a landmark study on the comparison of Bayesian and frequentist point estimators. Their findings indicate that Bayesian point estimators work well in more situations than were previously suspected. In particular, their comparison reveals how a Bayesian point estimator can improve upon a frequentist point estimator even in situations where sharp prior knowledge is not necessarily available. In the current paper, we show that similar results hold when comparing Bayesian and frequentist interval estimators. Furthermore, the development of an appropriate interval estimator comparison offers some further insight into the estimation problem.

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Gisler, Alois, and Mario V. Wüthrich. "Credibility for the Chain Ladder Reserving Method." ASTIN Bulletin 38, no. 02 (2008): 565–600. http://dx.doi.org/10.2143/ast.38.2.2033354.

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We consider the chain ladder reserving method in a Bayesian set up, which allows for combining the information from a specific claims development triangle with the information from a collective. That is, for instance, to consider simultaneously own company specific data and industry-wide data to estimate the own company's claims reserves. We derive Bayesian estimators and credibility estimators within this Bayesian framework. We show that the credibility estimators are exact Bayesian in the case of the exponential dispersion family with its natural conjugate priors. Finally, we make the link to the classical chain ladder method and we show that using non-informative priors we arrive at the classical chain ladder forecasts. However, the estimates for the mean square error of prediction differ in our Bayesian set up from the ones found in the literature. Hence, the paper also throws a new light upon the estimator of the mean square error of prediction of the classical chain ladder forecasts and suggests a new estimator in the chain ladder method.

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Gisler, Alois, and Mario V. Wüthrich. "Credibility for the Chain Ladder Reserving Method." ASTIN Bulletin 38, no. 2 (2008): 565–600. http://dx.doi.org/10.1017/s0515036100015294.

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Shojaee, Omid, Hassan Zarei, and Fatemeh Naruei. "E-Bayesian estimation and the corresponding E-MSE under progressive type-II censored data for some characteristics of Weibull distribution." Statistics, Optimization & Information Computing 12, no. 4 (2023): 962–81. http://dx.doi.org/10.19139/soic-2310-5070-1709.

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Estimating the parameters (or characteristics) of a distribution, from the availability of censored samples, is one of the most important topics in statistical inference over the past decades. This study is concerned about the E-Bayesian estimation method to compute the estimates of the parameter, the hazard rate function and the reliability function of the Weibull distribution when the progressive type-2 censored samples are available. The estimations are obtained based on the Squared error loss function (as a symmetric loss) and General Entropy and LINEX loss functions (as asymmetric losses). In addition, the asymptotic behaviour of the derived E-Bayesian estimators is discussed. Moreover, the E-Bayesian estimators under the different loss functions have been compared through Monte Carlo simulation studies by calculating the E-MSE of the resulting estimators, which is a new measure to compare the E-Bayesian estimators. As an application, we analyzed two real data sets that follow from the Weibull distribution.

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Keddali, Meriem, Hamida Talhi, Nawel Khodja, and Assia Chadli. "Bayesian robust analysis of the truncated XLindley distribution." STUDIES IN ENGINEERING AND EXACT SCIENCES 5, no. 2 (2024): e8849. http://dx.doi.org/10.54021/seesv5n2-302.

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In this study, we offer a robust analysis of the Bayesian estimators using the oscillation of posterior risks (PR) of the two parameters Upper truncated XLindley (UXLE) model, which is a novel variant of the Lindley model. We introduce the model together with its likelihood function in a censored scheme. Nonetheless, a relatively small number of writers addressed the subject of robustness and sensitivity analysis of the Bayesian estimators. For this reason, it can be said that there have only been a small number of applications produced in this area up to this point. The technique is explained using the oscillation of the Bayesian estimator’s posterior risks. Through the application of a Monte Carlo simulation study, we demonstrate that a robust Bayesian estimator of the parameters corresponding the smallest oscillation of the posterior risks maybe obtained under the right generalized loss function; when the parameters are not high, robust estimators can be obtained.

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Hassan, Amal Soliman, Elsayed Ahmed Elsherpieny, and Rokaya Elmorsy Mohamed. "Estimation of Information Measures for Power-Function Distribution in Presence of Outliers and Their Applications." Journal of Information and Communication Technology 21, No.1 (2021): 1–25. http://dx.doi.org/10.32890/jict2022.21.1.1.

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The measure of entropy has an undeniable pivotal role in the field of information theory. This article estimates the Rényi and q-entropies of the power function distribution in the presence of s outliers. The maximum likelihood estimators as well as the Bayesian estimators under uniform and gamma priors are derived. The proposed Bayesian estimators of entropies under symmetric and asymmetric loss functions are obtained. These estimators are computed empirically using Monte Carlo simulation based on Gibbs sampling. Outcomes of the study showed that the precision of the maximum likelihood and Bayesian estimates of both entropies measures improves with sample sizes. The behavior of both entropies estimates increase with number of outliers. Further, Bayesian estimates of the Rényi and q-entropies under squared error loss function are preferable than the other Bayesian estimates under the other loss functions in most of cases. Eventually, real data examples are analyzed to illustrate the theoretical results.

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He, Kexin, and Wenhao Gui. "Reliability Estimation for Burr XII Distribution under the Weighted Q-Symmetric Entropy Loss Function." Applied Sciences 14, no. 8 (2024): 3308. http://dx.doi.org/10.3390/app14083308.

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Considering that the choice of loss function plays a significant role in the derivation of Bayesian estimators, we propose a novel asymmetric loss function named the weighted Q-symmetric entropy loss for computing the estimates of the parameter and reliability function of the Burr XII distribution. This paper covers the classical maximum-likelihood, uniformly minimum-variance unbiased, and Bayesian estimation methods under the squared error loss, general entropy loss, Q-symmetric entropy loss, and new loss functions. Through Monte Carlo simulation, the respective performances of the considered estimators for the reliability function are evaluated, indicating that the Bayesian estimator under the new loss function is more efficient than those under other loss functions. Finally, a real data set is used to demonstrate the practicality of the presented estimators.

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Uma, Srivastava, and Kumar Harish. "Estimation of Cut Point in Burr III Sequence under Linear Exponential Loss." International Journal of Innovative Science and Research Technology 7, no. 7 (2022): 501–8. https://doi.org/10.5281/zenodo.6956269.

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This paper estimates the single cut-point in the mean of a Burr III Sequence and its scale parameters before and after the cut point. We introduce a strong estimator of the parameters with the help of Bayesian inference approach, by persevering these estimatorsin the criteria used to estimate the cut-point under Linear Exponential Loss Function. The simulation technique is used compare the estimators. Open-source R software is used in the simulation section. We have taken real data to estimate the parameters of the sequence and then hypothetical observations of the sequence to prove their robustness of the estimators.

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Alharbi, Yasser S., and Amr R. Kamel. "Fuzzy System Reliability Analysis for Kumaraswamy Distribution: Bayesian and Non-Bayesian Estimation with Simulation and an Application on Cancer Data Set." WSEAS TRANSACTIONS ON BIOLOGY AND BIOMEDICINE 19 (June 7, 2022): 118–39. http://dx.doi.org/10.37394/23208.2022.19.14.

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This paper proposes the fuzzy Bayesian (FB) estimation to get the best estimate of the unknown parameters of a two-parameter Kumaraswamy distribution from a frequentist point of view. These estimations of parameters are employed to estimate the fuzzy reliability function of the Kumaraswamy distribution and to select the best estimate of the parameters and fuzzy reliability function. To achieve this goal we investigate the efficiency of seven classical estimators and compare them with FB proposed estimation. Monte Carlo simulations and cancer data set applications are performed to compare the performances of the estimators for both small and large samples. Tierney and Kadane approximation is used to obtain FB estimates of traditional and fuzzy reliability for the Kumaraswamy distribution. The results showed that the fuzziness is better than the reality for all sample sizes and the fuzzy reliability at the estimates of the FB proposed estimated is better than other estimators, it gives the lowest Bias and root mean squared error.

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admin, admin. "On The Bayesian Estimation of Parameters of SQDM." Neutrosophic and Information Fusion 3, no. 1 (2024): 34–41. http://dx.doi.org/10.54216/nif.030105.

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This work is concerned with the problem of estimating parameters of spatial quadratic models by Bayesian technique (SQDM). This technique involves the prior information of the first and second moment of the parameters, where its estimation model is called the Bayesian quadratic unbiased estimator. The results of the estimation are taken in compared with the estimates of minimum norm quadratic unbiased estimators.

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Eldemery, E. M., A. M. Abd-Elfattah, K. M. Mahfouz, and Mohammed M. El Genidy. "Bayesian and E-Bayesian Estimation for the Generalized Rayleigh Distribution under Different Forms of Loss Functions with Real Data Application." Journal of Mathematics 2023 (August 31, 2023): 1–25. http://dx.doi.org/10.1155/2023/5454851.

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This paper investigates the estimation of an unknown shape parameter of the generalized Rayleigh distribution using Bayesian and expected Bayesian estimation techniques based on type-II censoring data. Subsequently, these estimators are obtained using four different loss functions: the linear exponential loss function, the weighted linear exponential loss function, the compound linear exponential loss function, and the weighted compound linear exponential loss function. The weighted compound linear exponential loss function is a novel suggested loss function generated by combining weights with the compound linear exponential loss function. We use the gamma distribution as a prior distribution. In addition, the expected Bayesian estimator is obtained through three different prior distributions of the hyperparameters. Moreover, depending on the four distinct forms of loss functions, Bayesian and expected Bayesian estimation techniques are performed using Monte Carlo simulations to verify the effectiveness of the suggested loss function and to compare Bayesian and expected Bayesian estimation methods. Furthermore, the simulation results indicate that, depending on the minimum mean squared error, the Bayesian and expected Bayesian estimations corresponding to the weighted compound linear exponential loss function suggested in this paper have significantly better performance compared to other loss functions, and the expected Bayesian estimator also performs better than the Bayesian estimator. Finally, the proposed techniques are demonstrated using a set of real data from the medical field to clarify the applicability of the suggested estimators to real phenomena and to show that the discussed weighted compound linear exponential loss function is efficient and can be applied in a real-life scenario.

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Naji, Loaiy F., and Huda Abdullah Rasheed. "Bayesian Estimation for Two Parameters of Gamma Distribution Under Precautionary Loss Function." Ibn AL- Haitham Journal For Pure and Applied Science 32, no. 1 (2019): 193. http://dx.doi.org/10.30526/32.1.1914.

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In the current study, the researchers have been obtained Bayes estimators for the shape and scale parameters of Gamma distribution under the precautionary loss function, assuming the priors, represented by Gamma and Exponential priors for the shape and scale parameters respectively. Moment, Maximum likelihood estimators and Lindley’s approximation have been used effectively in Bayesian estimation. Based on Monte Carlo simulation method, those estimators are compared depending on the mean squared errors (MSE’s). The results show that, the performance of Bayes estimator under precautionary loss function with Gamma and Exponential priors is better than other estimates in all cases.

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Kinyanjui, Josphat K., and Betty C. Korir. "Bayesian Estimation of Parameters of Weibull Distribution Using Linex Error Loss Function." International Journal of Statistics and Probability 9, no. 2 (2020): 38. http://dx.doi.org/10.5539/ijsp.v9n2p38.

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This paper develops a Bayesian analysis of the scale parameter in the Weibull distribution with a scale parameter&nbsp; &theta;&nbsp; and shape parameter&nbsp; &beta; (known). For the prior distribution of the parameter involved, inverted Gamma distribution has been examined. Bayes estimates of the scale parameter,&nbsp;&theta;&nbsp; , relative to LINEX loss function are obtained. Comparisons in terms of risk functions of those under LINEX loss and squared error loss functions with their respective alternate estimators, viz: Uniformly Minimum Variance Unbiased Estimator (U.M.V.U.E) and Bayes estimators relative to squared error loss function are made. It is found that Bayes estimators relative to squared error loss function dominate the alternative estimators in terms of risk function.

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M Hasaballah, Mustafa, Oluwafemi Samson Balogun, and M. E. Bakr. "Bayesian estimation for the power rayleigh lifetime model with application under a unified hybrid censoring scheme." Physica Scripta 99, no. 10 (2024): 105209. http://dx.doi.org/10.1088/1402-4896/ad72b2.

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Abstract This study presents a comprehensive analysis of Bayesian estimation techniques for the parameters of the power Rayleigh (PR) distribution under a unified hybrid censoring scheme (UHCS). The research employs both Bayesian and Frequentist approaches, utilizing maximum likelihood estimation (MLE) alongside Bayesian estimates derived through Markov Chain Monte Carlo (MCMC) methods. The study incorporates symmetric and asymmetric loss functions, specifically general entropy (GE), linear expoential (LINEX), and squared error (SE), to evaluate the performance of the estimators. A Monte Carlo simulation study is conducted to assess the effectiveness of the proposed methods, revealing that Bayesian estimators generally outperform Frequentist estimators in terms of mean squared error (MSE). Additionally, the paper includes a real-world application involving ball bearing lifetimes, demonstrating the practical utility of the proposed estimation techniques. The findings indicate that both point and interval estimates exhibit strong properties for parameter estimation, with Bayesian estimates being particularly favored for their accuracy and reliability.

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Savita, Savita, and Rajeev Kumar. "Dynamic Weighted Cumulative Residual Entropy Estimators for Laplace Distribution: Bayesian Approach." Indian Journal Of Science And Technology 17, no. 6 (2024): 556–65. http://dx.doi.org/10.17485/ijst/v17i6.1661.

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Objectives: To develop Bayesian estimators of dynamic weighted cumulative residual entropy (DWCRE) for Laplace distribution and to investigate posterior risks using various priors and loss functions. Methods: Weighted entropy measure of information is provided by a probabilistic experiment whose basic events are described by their objective probabilities and some qualitative (objective or subjective) weights. In this paper, we have used priors (Jeffrey’s, Hartigan, Uniform and Gumble Type II) and several loss functions. Findings: Bayesian estimators and associated posterior risks for Laplace distribution have been derived for different priors and loss functions. Monte Carlo Simulation study and graphical analyses have also been presented along with the conclusion. Through the comprehensive simulation study in the paper, it has been observed that Hartigan prior is better than other priors in terms of the posterior risk whereas Uniform prior has always higher posterior risk. Novelty: The introduction of new Bayesian estimators and their posterior risks for dynamic weighted cumulative residual entropy (DWCRE) of Laplace distribution. Keywords: Bayesian estimators, Laplace distribution, Fisher information matrix, Loss functions, Priors

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Alyami, Salem A., Amal S. Hassan, Ibrahim Elbatal, Olayan Albalawi, Mohammed Elgarhy, and Ahmed R. El-Saeed. "Bayesian and non-bayesian analysis for stress-strength model based on progressively first failure censoring with applications." PLOS ONE 19, no. 12 (2024): e0312937. https://doi.org/10.1371/journal.pone.0312937.

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This article examines the estimate of ϑ = P [T < Q], using both Bayesian and non-Bayesian methods, utilizing progressively first-failure censored data. Assume that the stress (T) and strength (Q) are independent random variables that follow the Burr III distribution and the Burr XII distribution, respectively, with a common first-shape parameter. The Bayes estimator and maximum likelihood estimator of ϑ are obtained. The maximum likelihood (ML) estimator is obtained for non-Bayesian estimation, and the accompanying confidence interval is constructed using the delta approach and the asymptotic normality of ML estimators. Through the use of non-informative and gamma informative priors, the Bayes estimator of ϑ under squared error and linear exponential loss functions is produced. It is suggested that Markov chain Monte Carlo techniques be used for Bayesian estimation in order to achieve Bayes estimators and the associated credible intervals. To evaluate the effectiveness of the several estimators created, a Monte Carlo numerical analysis is also carried out. In the end, for illustrative reasons, an algorithmic application to actual data is investigated.

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Reiss, R. D., and M. Thomas. "A New Class of Bayesian Estimators in Paretian Excess-of-Loss Reinsurance." ASTIN Bulletin 29, no. 2 (1999): 339–49. http://dx.doi.org/10.2143/ast.29.2.504620.

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AbstractFor estimating the shape parameter of Paretian excess claims, certain Bayesian estimators, which are closely related to the Hill estimator, have been suggested in the insurance literature. It turns out that these estimators may have a poor performance – just as the Hill estimator – if a certain location parameter is unequal to zero in the Paretian modeling. In an alternative formulation this means that a scale parameter is unequal to 1. Thus, it suggests itself to add the scale parameter in the modeling and to deal with Bayesian estimators of the shape and scale parameters in a full Paretian model. These estimators will be applied to fire and motor reinsurance data. The performance of these estimators will be illustrated by means of Monte Carlo simulations.

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Moura E Silva, Wyara Vanesa, and Daniel Leonardo Ramírez Orozco. "Evaluación de rendimiento de los estimadores para los parámetros de la Distribución Burr XII." Comunicaciones en Estadística 15, no. 1 (2022): 1–14. https://doi.org/10.15332/23393076.7755.

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The main objective of this paper is to evaluate the performance of maximum likelihood estimators and Bayesian point estimators for the parameters p and b of the Burr XII distribution and its bootstrap-corrected versions. Monte Carlo simulations were used for the analysis, considering various scenarios and verifying some properties of these estimators, such as the mean, variance, bias, and mean squared error. The corrected estimators presented better performances in terms of the estimation by the maximum likelihood method, the same does not happen in the point estimates for the analysis of the Bayesian estimators.

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Cocchi, Daniela, Lorenzo Marchi, and Riccardo Ievoli. "Bayesian Bootstrap in Multiple Frames." Stats 5, no. 2 (2022): 561–71. http://dx.doi.org/10.3390/stats5020034.

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Multiple frames are becoming increasingly relevant due to the spread of surveys conducted via registers. In this regard, estimators of population quantities have been proposed, including the multiplicity estimator. In all cases, variance estimation still remains a matter of debate. This paper explores the potential of Bayesian bootstrap techniques for computing such estimators. The suitability of the method, which is compared to the existing frequentist bootstrap, is shown by conducting a small-scale simulation study and a case study.

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Yousef, Manal M., Aisha Fayomi, and Ehab M. Almetwally. "Simulation Techniques for Strength Component Partially Accelerated to Analyze Stress–Strength Model." Symmetry 15, no. 6 (2023): 1183. http://dx.doi.org/10.3390/sym15061183.

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Based on independent progressive type-II censored samples from two-parameter Burr-type XII distributions, various point and interval estimators of δ=P(Y<X) were proposed when the strength variable was subjected to the step–stress partially accelerated life test. The point estimators computed were maximum likelihood and Bayesian under various symmetric and asymmetric loss functions. The interval estimations constructed were approximate, bootstrap-P, and bootstrap-T confidence intervals, and a Bayesian credible interval. A Markov Chain Monte Carlo approach using Gibbs sampling was designed to derive the Bayesian estimate of δ. Based on the mean square error, bias, confidence interval length, and coverage probability, the results of the numerical analysis of the performance of the maximum likelihood and Bayesian estimates using Monte Carlo simulations were quite satisfactory. To support the theoretical component, an empirical investigation based on two actual data sets was carried out.

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Entropy measurement plays an important role in the field of information theory. Furthermore, the estimation of entropy is an important issue in statistics and machine learning. This study estimated the Rényi and q-entropies of a power-function distribution in the presence of s outliers using classical and Bayesian procedures. In the classical method, the maximum likelihood estimators of the entropies were obtained and their performance was assessed through a numerical study. In the Bayesian method, the Bayesian estimators of the entropies under uniform and gamma priors were acquired based on different loss functions. The Bayesian estimators were computed empirically using a Monte Carlo simulation based on the Gibbs sampling algorithm. The simulated datasets were analyzed to investigate the accuracy of the estimates. The study results showed that the precision of the maximum likelihood and Bayesian estimates of both entropies improved with increasing the sample size and the number of outliers. The absolute biases and the mean squared errors of the estimates in the presence of outliers exceeded those of the corresponding estimates in the homogenous case (no-outliers). Furthermore, the Bayesian estimates of the Rényi and q-entropies under the squared error loss function were preferable to the other Bayesian estimates in a majority of the cases. Finally, analysis results of real data examples were consistent with those of the simulated data.

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Abbas, Kamran, Nosheen Yousaf Abbasi, Amjad Ali, et al. "Bayesian Analysis of Three-Parameter Frechet Distribution with Medical Applications." Computational and Mathematical Methods in Medicine 2019 (March 12, 2019): 1–8. http://dx.doi.org/10.1155/2019/9089856.

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The medical data are often filed for each patient in clinical studies in order to inform decision-making. Usually, medical data are generally skewed to the right, and skewed distributions can be the appropriate candidates in making inferences using Bayesian framework. Furthermore, the Bayesian estimators of skewed distribution can be used to tackle the problem of decision-making in medicine and health management under uncertainty. For medical diagnosis, physician can use the Bayesian estimators to quantify the effects of the evidence in increasing the probability that the patient has the particular disease considering the prior information. The present study focuses the development of Bayesian estimators for three-parameter Frechet distribution using noninformative prior and gamma prior under LINEX (linear exponential) and general entropy (GE) loss functions. Since the Bayesian estimators cannot be expressed in closed forms, approximate Bayesian estimates are discussed via Lindley’s approximation. These results are compared with their maximum likelihood counterpart using Monte Carlo simulations. Our results indicate that Bayesian estimators under general entropy loss function with noninformative prior (BGENP) provide the smallest mean square error for all sample sizes and different values of parameters. Furthermore, a data set about the survival times of a group of patients suffering from head and neck cancer is analyzed for illustration purposes.

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Tresp, Volker. "A Bayesian Committee Machine." Neural Computation 12, no. 11 (2000): 2719–41. http://dx.doi.org/10.1162/089976600300014908.

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The Bayesian committee machine (BCM) is a novel approach to combining estimators that were trained on different data sets. Although the BCM can be applied to the combination of any kind of estimators, the main foci are gaussian process regression and related systems such as regularization networks and smoothing splines for which the degrees of freedom increase with the number of training data. Somewhat surprisingly, we find that the performance of the BCM improves if several test points are queried at the same time and is optimal if the number of test points is at least as large as the degrees of freedom of the estimator. The BCM also provides a new solution for on-line learning with potential applications to data mining. We apply the BCM to systems with fixed basis functions and discuss its relationship to gaussian process regression. Finally, we show how the ideas behind the BCM can be applied in a non-Bayesian setting to extend the input-dependent combination of estimators.

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Asteris, Georgios, and Sahotra Sarkar. "Bayesian Procedures for the Estimation of Mutation Rates from Fluctuation Experiments." Genetics 142, no. 1 (1996): 313–26. http://dx.doi.org/10.1093/genetics/142.1.313.

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Bayesian procedures are developed for estimating mutation rates from fluctuation experiments. Three Bayesian point estimators are compared with four traditional ones using the results of 10,000 simulated experiments. The Bayesian estimators were found to be at least as efficient as the best of the previously known estimators. The best Bayesian estimator is one that uses (1/m 2) as the prior probability density function and a quadratic loss function. The advantage of using these estimators is most pronounced when the number of fluctuation test tubes is small. Bayesian estimation allows the incorporation of prior knowledge about the estimated parameter, in which case the resulting estimators are the most efficient. It enables the straightfonvard construction of confidence intervals for the estimated parameter. The increase of efficiency with prior information and the narrowing of the confidence intervals with additional experimental results are investigated. The results of the simulations show that any potential inaccuracy of estimation arising from lumping together all cultures with more than n mutants (the jackpots) almost disappears at n = 70 (provided that the number of mutations in a culture is low). These methods are applied to a set of experimental data to illustrate their use.

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Awad, Manahel Kh, and Huda A. Rasheed. "Estimation of the Reliability Function of Basic Gompertz Distribution under Different Priors." Ibn AL- Haitham Journal For Pure and Applied Sciences 33, no. 3 (2020): 167. http://dx.doi.org/10.30526/33.3.2482.

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In this paper, some estimators for the reliability function R(t) of Basic Gompertz (BG) distribution have been obtained, such as Maximum likelihood estimator, and Bayesian estimators under General Entropy loss function by assuming non-informative prior by using Jefferys prior and informative prior represented by Gamma and inverted Levy priors. Monte-Carlo simulation is conducted to compare the performance of all estimates of the R(t), based on integrated mean squared.

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Reyad, Hesham, Adil Younis, and Amal Alkhedir. "Quasi-E-Bayesian criteria versus quasi-Bayesian, quasi-hierarchical Bayesian and quasi-empirical Bayesian methods for estimating the scale parameter of the Erlang distribution." International Journal of Advanced Statistics and Probability 4, no. 1 (2016): 62. http://dx.doi.org/10.14419/ijasp.v4i1.6095.

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This paper proposes a new modification for the E-Bayesian method of estimation to introduce a new technique namely Quasi E-Bayesian method (or briefly QE-Bayesian). The suggested criteria built in replacing the likelihood function by the quasi likelihood function in the E-Bayesian technique. This study is devoted to evaluate the performance of the new method versus the quasi-Bayesian, quasi-hierarchical Bayesian and quasi-empirical Bayesian approaches in estimating the scale parameter of the Erlang distribution. All estimators are obtained under symmetric loss function [squared error loss (SELF))] and four different asymmetric loss functions [Precautionary loss function (PLF), entropy loss function (ELF), Degroot loss function (DLF) and quadratic loss function (QLF)]. The properties of the QE-Bayesian estimates are introduced and the relations between the QE-Bayes and quasi-hierarchical Bayes estimates are discussed. Comparisons among all estimators are performed in terms of mean square error (MSE) via Monte Carlo simulation.

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Cai, Yuxin, and Wenhao Gui. "Classical and Bayesian Inference for a Progressive First-Failure Censored Left-Truncated Normal Distribution." Symmetry 13, no. 3 (2021): 490. http://dx.doi.org/10.3390/sym13030490.

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Point and interval estimations are taken into account for a progressive first-failure censored left-truncated normal distribution in this paper. First, we derive the estimators for parameters on account of the maximum likelihood principle. Subsequently, we construct the asymptotic confidence intervals based on these estimates and the log-transformed estimates using the asymptotic normality of maximum likelihood estimators. Meanwhile, bootstrap methods are also proposed for the construction of confidence intervals. As for Bayesian estimation, we implement the Lindley approximation method to determine the Bayesian estimates under not only symmetric loss function but also asymmetric loss functions. The importance sampling procedure is applied at the same time, and the highest posterior density (HPD) credible intervals are established in this procedure. The efficiencies of classical statistical and Bayesian inference methods are evaluated through numerous simulations. We conclude that the Bayes estimates given by Lindley approximation under Linex loss function are highly recommended and HPD interval possesses the narrowest interval length among the proposed intervals. Ultimately, we introduce an authentic dataset describing the tensile strength of 50mm carbon fibers as an illustrative sample.

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Hassan, Amal S., Najwan Alsadat, Oluwafemi Samson Balogun, and Baria A. Helmy. "Bayesian and non-Bayesian estimation of some entropy measures for a Weibull distribution." AIMS Mathematics 9, no. 11 (2024): 32646–73. http://dx.doi.org/10.3934/math.20241563.

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Entropy measures have been employed in various applications as a helpful indicator of information content. This study considered the estimation of Shannon entropy, $ \zeta $-entropy, Arimoto entropy, and Havrda and Charvat entropy measures for the Weibull distribution. The classical and Bayesian estimators for the suggested entropy measures were derived using generalized Type Ⅱ hybrid censoring data. Based on symmetric and asymmetric loss functions, Bayesian estimators of entropy measurements were developed. Asymptotic confidence intervals with the help of the delta method and the highest posterior density intervals of entropy measures were constructed. The effectiveness of the point and interval estimators was evaluated through a Monte Carlo simulation study and an application with actual data sets. Overall, the study's results indicate that with longer termination times, both maximum likelihood and Bayesian entropy estimates were effective. Furthermore, Bayesian entropy estimates using the linear exponential loss function tended to outperform those using other loss functions in the majority of scenarios. In conclusion, the analysis results from real-world examples aligned with the simulated data. Drawing insights from the analysis of glass fiber, we can assert that this research holds practical applications in reliability engineering and financial analysis.

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Mohamed, Nur Anisah, Ayed R. A. Alanzi, Azlinna Noor Azizan, Suzana Ariff Azizan, Nadia Samsudin, and Hashem Salarzadeh Jenatabadi. "Application of Bayesian structural equation modeling in construction and demolition waste management studies: Development of an extended theory of planned behavior." PLOS ONE 19, no. 1 (2024): e0290376. http://dx.doi.org/10.1371/journal.pone.0290376.

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Sustainable construction and demolition waste management relies heavily on the attitudes and actions of its constituents; nevertheless, deep analysis for introducing the best estimator is rarely attained. The main objective of this study is to perform a comparison analysis among different approaches of Structural Equation Modeling (SEM) in Construction and Demolition Waste Management (C&DWM) modeling based on an Extended Theory of Planned Behaviour (Extended TPB). The introduced research model includes twelve latent variables, six independent variables, one mediator, three control variables, and one dependent variable. Maximum likelihood (ML), partial least square (PLS), and Bayesian estimators were considered in this study. The output of SEM with the Bayesian estimator was 85.8%, and among effectiveness of six main variables on C&DWM Behavioral (Depenmalaydent variables), five of them have significant relations. Meanwhile, the variation based on SEM with ML estimator was equal to 78.2%, and four correlations with dependent variable have significant relationship. At the conclusion, the R-square of SEM with the PLS estimator was equivalent to 73.4% and three correlations with the dependent variable had significant relationships. At the same time, the values of the three statistical indices include root mean square error (RMSE), mean absolute percentage error (MPE), and mean absolute error (MSE) with involving Bayesian estimator are lower than both ML and PLS estimators. Therefore, compared to both PLS and ML, the predicted values of the Bayesian estimator are closer to the observed values. The lower values of MPE, RMSE, and MSE and the higher values of R-square will generate better goodness of fit for SEM with a Bayesian estimator. Moreover, the SEM with a Bayesian estimator revealed better data fit than both the PLS and ML estimators. The pattern shows that the relationship between research variables can change with different estimators. Hence, researchers using the SEM technique must carefully consider the primary estimator for their data analysis. The precaution is necessary because higher error means different regression coefficients in the research model.

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Liu, Shuhan, and Wenhao Gui. "Estimating the Parameters of the Two-Parameter Rayleigh Distribution Based on Adaptive Type II Progressive Hybrid Censored Data with Competing Risks." Mathematics 8, no. 10 (2020): 1783. http://dx.doi.org/10.3390/math8101783.

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This paper attempts to estimate the parameters for the two-parameter Rayleigh distribution based on adaptive Type II progressive hybrid censored data with competing risks. Firstly, the maximum likelihood function and the maximum likelihood estimators are derived before the existence and uniqueness of the latter are proven. Further, Bayesian estimators are considered under symmetric and asymmetric loss functions, that is the squared error loss function, the LINEXloss function, and the general entropy loss function. As the Bayesian estimators cannot be obtained explicitly, the Lindley method is applied to compute the approximate Bayesian estimates. Finally, a simulation study is conducted, and a real dataset is analyzed for illustrative purposes.

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Ozguven, Eren Erman, and Kaan Ozbay. "Nonparametric Bayesian Estimation of Freeway Capacity Distribution from Censored Observations." Transportation Research Record: Journal of the Transportation Research Board 2061, no. 1 (2008): 20–29. http://dx.doi.org/10.3141/2061-03.

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Previous studies have been made of the usefulness and effectiveness of survival analysis in transportation and traffic engineering studies with incomplete data in which the Kaplan–Meier estimate is proposed for determining traffic capacity distribution. However, well-known estimators like Kaplan–Meier and Nelson–Aalen have several disadvantages that make it difficult to obtain the traffic capacity distribution. First, neither estimator is defined for all values of traffic flows possible. That is, the maximum flow followed by a breakdown defines the final point of the estimated distribution curve. Therefore, parametric fitting tools have to be applied to obtain the remaining portion of the curve. Moreover, the discontinuity and nonsmoothness of the Kaplan–Meier and Nelson–Aalen estimates make it difficult to ensure the robustness of the estimation. In this paper the Kaplan–Meier and Nelson–Aalen nonparametric estimators are used to obtain the traffic capacity function of four freeway sections. Then a Bayesian nonparametric estimator, which is shown to be a Bayesian extension of the Kaplan–Meier estimator, is introduced for estimating the capacity distribution. This estimator assumes a Dirichlet process prior for the survival function under the minimization of a squared-error loss function. The results indicate that the curves obtained by using the Bayesian estimation method are smoother than those obtained with the other estimator. This smoothness also ensures the continuity in the vicinity of censored observations. Furthermore, the Bayesian estimates can be obtained for any traffic flow value regardless of the availability of data only for certain ranges of observations (including censored data).

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Xiao, Shixiao, Xue Hu, and Haiping Ren. "Estimation of Lifetime Performance Index for Generalized Inverse Lindley Distribution Under Adaptive Progressive Type-II Censored Lifetime Test." Axioms 13, no. 10 (2024): 727. http://dx.doi.org/10.3390/axioms13100727.

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The lifetime performance index (LPI) is an important metric for evaluating product quality, and research on the statistical inference of the LPI is of great significance. This paper discusses both the classical and Bayesian estimations of the LPI under an adaptive progressive type-II censored lifetime test, assuming that the product’s lifetime follows a generalized inverse Lindley distribution. At first, the maximum likelihood estimator of the LPI is derived, and the Newton–Raphson iterative method is adopted to solve the numerical solution due to the log-likelihood equations having no analytical solutions. If the exact distribution of the LPI is not available, then the asymptotic confidence interval and bootstrap confidence interval of the LPI are constructed. For the Bayesian estimation, the Bayesian estimators of the LPI are derived under three different loss functions. Due to the complex multiple integrals involved in these estimators, the MCMC method is used to draw samples and further construct the HPD credible interval of the LPI. Finally, Monte Carlo simulations are used to observe the performance of these estimators in terms of the average bias and mean squared error, and two practical examples are used to illustrate the application of the proposed estimation method.

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Elbatal, Ibrahim, Naif Alotaibi, Salem A. Alyami, Mohammed Elgarhy, and Ahmed R. El-Saeed. "Bayesian and Non-Bayesian Estimation of the Nadaraj ah–Haghighi Distribution: Using Progressive Type-1 Censoring Scheme." Mathematics 10, no. 5 (2022): 760. http://dx.doi.org/10.3390/math10050760.

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This work will address the problem of estimating the parameters for the Nadaraj ah–Haghighi (NH) distribution using progressive Type-1 censoring (PT1C) utilizing Bayesian and non-Bayesian approaches. To apply PT1C, censoring times for each stage of censoring needed to be known before the experiment started. To solve this issue of censoring time selection, qauntiles from the NH lifetime distribution will be used as PT1C censoring time points. Maximum likelihood (ML) estimators (MLEs) and asymptotic confidence intervals (ACoIs) are produced with a focus on the censoring technique. Bayes estimates (BEs) and accompanying maximum posterior density (PD) credible interval estimations are also created via the squared error (SEr) loss function. The BEs are evaluated using the Markov Chain Monte Carlo (MCMC) technique and the Metropolis–Hasting (MH) algorithm. An analysis of an actual data set demonstrates the theoretical implications of MLEs and BEs for defined schemes of PT1C samples. Finally, simulation results will be used to compare the performance of the various recommended estimators.

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Yi, Zhang, Wen Limin, and Li Zhilong. "The Bühlmann–Straub Estimation of Claim Means in Random B-F Reserve Model." Mathematical Problems in Engineering 2020 (May 7, 2020): 1–11. http://dx.doi.org/10.1155/2020/6062906.

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In the B-F reserve model, it is a very critical step to estimate the claim means of the accident year. However, the traditional method uses the prior estimators of the claim means based on the personal experience of actuaries or historical data. This method inevitably carries the subjectivity of the actuary himself. In this paper, a stochastic B-F model is established, and a prior distribution is constructed for the claim means in the accident year. The idea of the credibility theory is used to derive the linear Bayesian estimators of claim means. Finally, the empirical Bayesian method is used to estimate the first two moments of the prior distribution, and the empirical Bayesian estimators of the claim means and the corresponding reserves are derived. The estimators obtained in this paper do not depend on the specific forms of the sample distribution and the prior distribution and can be used directly in practice. In the numerical simulation, our estimates are compared with the traditional B-F estimates and the chain ladder estimates. It is verified that the estimates given in this paper have small mean square error.

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Tu, Jiayi, and Wenhao Gui. "Bayesian Inference for the Kumaraswamy Distribution under Generalized Progressive Hybrid Censoring." Entropy 22, no. 9 (2020): 1032. http://dx.doi.org/10.3390/e22091032.

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Incomplete data are unavoidable for survival analysis as well as life testing, so more and more researchers are beginning to study censoring data. This paper discusses and considers the estimation of unknown parameters featured by the Kumaraswamy distribution on the condition of generalized progressive hybrid censoring scheme. Estimation of reliability is also considered in this paper. To begin with, the maximum likelihood estimators are derived. In addition, Bayesian estimators under not only symmetric but also asymmetric loss functions, like general entropy, squared error as well as linex loss function, are also offered. Since the Bayesian estimates fail to be of explicit computation, Lindley approximation, as well as the Tierney and Kadane method, is employed to obtain the Bayesian estimates. A simulation research is conducted for the comparison of the effectiveness of the proposed estimators. A real-life example is employed for illustration.

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AKDAM, Neriman. "Bayesian Analysis for the Modified Frechet–Exponential Distribution with Covid-19 Application." Cumhuriyet Science Journal 44, no. 3 (2023): 602–9. http://dx.doi.org/10.17776/csj.1320712.

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In this manuscript, the maximum likelihood estimators and Bayes estimators for the parameters of the modified Frechet–exponential distribution. Because the Bayes estimators cannot be obtained in closed forms, the approximate Bayes estimators are computed using the idea of Lindley’s approximation method under squared-error loss function. Then, the approximate Bayes estimates are compared with the maximum likelihood estimates in terms of mean square error and bias values using Monte Carlo simulation. Finally, real data sets belonging to COVID-19 death cases in Europe and China to are used to demonstrate the emprical results belonging to the approximate Bayes estimates, the maximum likelihood estimates.

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Okasha, Hassan M., Abdulkareem M. Basheer, and Yuhlong Lio. "The E-Bayesian Methods for the Inverse Weibull Distribution Rate Parameter Based on Two Types of Error Loss Functions." Mathematics 10, no. 24 (2022): 4826. http://dx.doi.org/10.3390/math10244826.

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Given a sample, E-Bayesian estimates, which are the expected Bayesian estimators over the joint distributions of two hyperparameters in the prior distribution, are developed for the inverse Weibull distribution rate parameter under the scaled squared error and linear exponential error loss functions, respectively. The corresponding expected mean square errors, EMSEs, of E-Bayesian estimators based on the sample are derived. Moreover, the theoretical properties of EMSEs are established. A Monte Carlo simulation study is conducted for the performance comparison. Finally, three data sets are given for illustration.

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Yassen, Mansour F., Fuad S. Al-Duais, and Mohammed M. A. Almazah. "Ridge Regression Method and Bayesian Estimators under Composite LINEX Loss Function to Estimate the Shape Parameter in Lomax Distribution." Computational Intelligence and Neuroscience 2022 (August 29, 2022): 1–10. http://dx.doi.org/10.1155/2022/1200611.

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In this paper, the Ridge Regression method is employed to estimate the shape parameter of the Lomax distribution (LD). In addition to that, the approaches of both classical and Bayesian are considered with several loss functions as a squared error (SELF), Linear Exponential (LLF), and Composite Linear Exponential (CLLF). As far as Bayesian estimators are concerned, informative and noninformative priors are used to estimate the shape parameter. To examine the performance of the Ridge Regression method, we compared it with classical estimators which included Maximum Likelihood, Ordinary Least Squares, Uniformly Minimum Variance Unbiased Estimator, and Median Method as well as Bayesian estimators. Monte Carlo simulation compares these estimators with respect to the Mean Square Error criteria (MSE’s). The result of the simulation mentioned that the Ridge Regression method is promising and can be used in a real environment. where it revealed better performance the than Ordinary Least Squares method for estimating shape parameter.

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Jurećková, Jana, and Lev B. Klebanov. "Trimmed, Bayesian and admissible estimators." Statistics & Probability Letters 42, no. 1 (1999): 47–51. http://dx.doi.org/10.1016/s0167-7152(98)00187-4.

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Singh, S. P. "On Bayesian Estimation of Maxwell Distribution under Precautionary Loss Function." Journal of the Tensor Society 9, no. 01 (2007): 1–7. http://dx.doi.org/10.56424/jts.v9i01.10571.

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In this paper Bayes estimator of the scale parameter of Maxwell distribution has been obtained by taking quasi, inverted gamma and uniform prior distributions using precautionary loss function. These estimators are compared with the corresponding Bayes estimators under squared error loss function.

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Ashour, Samir K., Ahmed A. El-Sheikh, and Ahmed Elshahhat. "Inferences for Weibull parameters under progressively first-failure censored data with binomial random removals." Statistics, Optimization & Information Computing 9, no. 1 (2020): 47–60. http://dx.doi.org/10.19139/soic-2310-5070-611.

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In this paper, the Bayesian and non-Bayesian estimation of a two-parameter Weibull lifetime model in presence of progressive first-failure censored data with binomial random removals are considered. Based on the s-normal approximation to the asymptotic distribution of maximum likelihood estimators, two-sided approximate confidence intervals for the unknown parameters are constructed. Using gamma conjugate priors, several Bayes estimates and associated credible intervals are obtained relative to the squared error loss function. Proposed estimators cannot be expressed in closed forms and can be evaluated numerically by some suitable iterative procedure. A Bayesian approach is developed using Markov chain Monte Carlo techniques to generate samples from the posterior distributions and in turn computing the Bayes estimates and associated credible intervals. To analyze the performance of the proposed estimators, a Monte Carlo simulation study is conducted. Finally, a real data set is discussed for illustration purposes.

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Khalid Hussein, Lamyaa, and Nadia Hashim Al-Noor. "Simulation Study for Estimating the Parameters and Reliability Function of Weighted Exponential Distribution with Fuzzy Data." Al-Nahrain Journal of Science 27, no. 2 (2024): 145–54. http://dx.doi.org/10.22401/anjs.27.2.15.

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This paper investigates the estimation of the two unknown parameters and the reliability function of the weighted exponential distribution. It explores Bayesian and non-Bayesian (maximum likelihood) estimation methods when the information availableisin the form of fuzzy data. The Newton-Raphson algorithm is used to obtain the maximum likelihood estimates. In Bayes estimation, the symmetric squared error loss function is used. This loss function linksequalimportance to the losses due to overestimating and underestimating equal magnitude. Lindley approximation procedure in Bayesian estimation theory is used to evaluate the ratio of integrals. A comparative analysis using simulation is carried out to evaluate the performance of the obtained parameters estimators using mean squared error criteria and the performance of the obtained reliability estimators using integrated mean squared error criteria. The simulation results demonstrate that, for different sample sizes, the performance of Bayes estimates surpasses the maximum likelihood, and that all estimators perform consistently

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Adepetun, A. O., and A. A. Adewara. "Bayesian Analysis of Warners Randomized Response Technique." Journal of Scientific Research 9, no. 1 (2017): 13–26. http://dx.doi.org/10.3329/jsr.v1i1.27943.

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This paper proposed alternative beta estimators of the population proportion of a sensitive attribute when life data were obtained through the administration of survey questionnaires on abortion of some matured women. The results showed that the proposed alternative beta estimators were more efficient in capturing responses from respondents than the simple beta estimator proposed by Winkler and Franklin for relatively small, medium as well as large sample sizes respectively.

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ناصر, جنان عباس. "Comparison Bayes Estimators of Reliability in the Exponential Distribution." Journal of Economics and Administrative Sciences 24, no. 104 (2018): 1. http://dx.doi.org/10.33095/jeas.v24i104.99.

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Abstract We produced a study in Estimation for Reliability of the Exponential distribution based on the Bayesian approach. These estimates are derived using Bayesian approaches. In the Bayesian approach, the parameter of the Exponential distribution is assumed to be random variable .we derived bayes estimators of reliability under four types when the prior distribution for the scale parameter of the Exponential distribution is: Inverse Chi-square distribution, Inverted Gamma distribution, improper distribution, Non-informative distribution. And estimators for Reliability is obtained using the well known squared error loss function and weighted squared errors loss function. We used simulation technique, to compare the resultant estimators in terms of their mean squared errors (MSE), mean weighted squared errors (MWSE).Several cases assumed for the parameter of the exponential distribution for data generating, of different samples sizes (small, medium, and large). The results were obtained by using simulation technique, Programs written using MATLAB-R2008a program were used. In general, Simulation results shown that the resultant estimators in terms of their mean squared errors (MSE) is better than the resultant estimators in terms of their mean weighted squared errors (MWSE).According to the our criteria is the best estimator that gives the smallest value of MSE or MWSE . For example bayes estimation is the best when the prior distribution for the scale parameter is improper and Non-informative distributions according to the smallest value of MSE comparative to the values of MWSE for all samples sizes at some of true value of t and . 

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H., Jayakrishna Udupa. "Estimation of Steady State Probability Distribution of System Size in M/M/1 Queue." Mapana - Journal of Sciences 8, no. 2 (2009): 20–28. http://dx.doi.org/10.12723/mjs.15.3.

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Recently Choudhury and Borthakur (2008) obtained classical and Bayesian estimators of performance measures based on a random sample of size n from a geometric distribution with mean ρ / (1− ρ) , which is the steady state probability distribution of system size. Here weobtain classical estimators, the Maximum Likelihood (ML) and Uniformly Minimum Variance Unbiased (UMVU) estimators, and Bayesian estimators of Pk , k=0,1,2,.... relative to beta prior distribution and Weighted Squared Error Loss (WSEL) function as well as relative to Standard Two-Sided Power (STSP) distribution and squared error loss / WSEL functions. Bayes, ML and UMVU estimates of the probability that the server is idle are also computed. Also Consistent Asymptotic Normality (CAN) for Pk , k=0,1,2,.... are examined.

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Khodja, N., H. Aiachi, H. Talhi, and I. N. Benatallah. "THE TRUNCATED XLINDLEY DISTRIBUTION WITH CLASSIC AND 6BAYESIAN INFERENCE UNDER CENSORED DATA." Advances in Mathematics: Scientific Journal 11, no. 12 (2022): 1191–207. http://dx.doi.org/10.37418/amsj.11.12.4.

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We provide a brand-new distribution based on the model of Lindley, with an emphasis on the estimation of its unknown parameters. After introducing the new distribution, we cover two approaches to estimate its parameters; in the presence of a censored scheme, we first use a traditional approach, which is The maximum likelihood technique, then we use the Bayesian approach. The BarzilaiBrown algorithm is used to derive the censored maximum likelihood estimators while a Monte Carlo Markov chains (MCMC) procedure is applied to derive the Bayesian ones. Three loss functions are used to provide the Bayesian estimators: the entropy, the generalized quadratic, and the Linex functions. Using Pitman's proximity criteria; the maximum likelihood and the Bayesian estimations are compared. All of the provided estimations techniques have been evaluated throughout simulation studies. Finally, we consider two sample Bayes predictions to predict future order statistics

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Reyad, Hesham, Adil Mousa Younis, and Amal Alsir Alkhedir. "Comparison of estimates using censored samples from Gompertz model: Bayesian, E-Bayesian, hierarchical Bayesian and empirical Bayesian schemes." International Journal of Advanced Statistics and Probability 4, no. 1 (2016): 47. http://dx.doi.org/10.14419/ijasp.v4i1.5914.

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This paper aims to introduce a comparative study for the E-Bayesian criteria with three various Bayesian approaches; Bayesian, hierarchical Bayesian and empirical Bayesian. This study is concerned to estimate the shape parameter and the hazard function of the Gompertz distribution based on type-II censoring. All estimators are obtained under symmetric loss function [squared error loss (SELF))] and three different asymmetric loss functions [quadratic loss function (QLF), entropy loss function (ELF) and LINEX loss function (LLF)]. Comparisons among all estimators are achieved in terms of mean square error (MSE) via Monte Carlo simulation.

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Alotaibi, Naif, Ibrahim Elbatal, Ehab M. Almetwally, Salem A. Alyami, A. S. Al-Moisheer, and Mohammed Elgarhy. "Truncated Cauchy Power Weibull-G Class of Distributions: Bayesian and Non-Bayesian Inference Modelling for COVID-19 and Carbon Fiber Data." Mathematics 10, no. 9 (2022): 1565. http://dx.doi.org/10.3390/math10091565.

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The Truncated Cauchy Power Weibull-G class is presented as a new family of distributions. Unique models for this family are presented in this paper. The statistical aspects of the family are explored, including the expansion of the density function, moments, incomplete moments (IMOs), residual life and reversed residual life functions, and entropy. The maximum likelihood (ML) and Bayesian estimations are developed based on the Type-II censored sample. The properties of Bayes estimators of the parameters are studied under different loss functions (squared error loss function and LINEX loss function). To create Markov-chain Monte Carlo samples from the posterior density, the Metropolis–Hasting technique was used with posterior density. Using non-informative and informative priors, a full simulation technique was carried out. The maximum likelihood estimator was compared to the Bayesian estimators using Monte Carlo simulation. To compare the performances of the suggested estimators, a simulation study was carried out. Real-world data sets, such as strength measured in GPA for single carbon fibers and impregnated 1000-carbon fiber tows, maximum stress per cycle at 31,000 psi, and COVID-19 data were used to demonstrate the relevance and flexibility of the suggested method. The suggested models are then compared to comparable models such as the Marshall–Olkin alpha power exponential, the extended odd Weibull exponential, the Weibull–Rayleigh, the Weibull–Lomax, and the exponential Lomax distributions.

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Ren, Hai Ping, and Jin Ping Li. "Bayes Estimation of Traffic Intensity in M/M/1 Queue under a New Weighted Square Error Loss Function." Advanced Materials Research 485 (February 2012): 490–93. http://dx.doi.org/10.4028/www.scientific.net/amr.485.490.

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Bayesian estimator of the traffic intensity in an M/M/1 queue is derived under a new weighted square error loss function. The Bayes estimators are obtained by using two different priors of the traffic intensity,namely,quasi-prior and beta prior. Finally, a Monte Carelo numerical simulation is used to compare these Bayes estimators with the corresponding maximum likelihood estimators.

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