Log in

Relevant bibliographies by topics / LINEX and quadratic loss functions / Journal articles

To see the other types of publications on this topic, follow the link: LINEX and quadratic loss functions.

Journal articles on the topic 'LINEX and quadratic loss functions'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'LINEX and quadratic loss functions.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Jaheen, Z. F. "Empirical Bayes analysis of record statistics based on linex and quadratic loss functions." Computers & Mathematics with Applications 47, no. 6-7 (March 2004): 947–54. http://dx.doi.org/10.1016/s0898-1221(04)90078-8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Reyad, Hesham, and Soha Othman Ahmed. "Bayesian and E-Bayesian estimation for the Kumaraswamy distribution based on type-ii censoring." International Journal of Advanced Mathematical Sciences 4, no. 1 (March 5, 2016): 10. http://dx.doi.org/10.14419/ijams.v4i1.5750.

Full text

Abstract:

<p>This paper introduces the Bayesian and E-Bayesian estimation for the shape parameter of the Kumaraswamy distribution based on type-II censored schemes. These estimators are derived under symmetric loss function [squared error loss (SELF))] and three asymmetric loss functions [LINEX loss function (LLF), Degroot loss function (DLF) and Quadratic loss function (QLF)]. Monte Carlo simulation is performed to compare the E-Bayesian estimators with the associated Bayesian estimators in terms of Mean Square Error (MSE).</p>

APA, Harvard, Vancouver, ISO, and other styles

3

Reyad, Hesham, and Soha Othman Ahmed. "E-Bayesian analysis of the Gumbel type-ii distribution under type-ii censored scheme." International Journal of Advanced Mathematical Sciences 3, no. 2 (September 5, 2015): 108. http://dx.doi.org/10.14419/ijams.v3i2.5093.

Full text

Abstract:

<p>This paper seeks to focus on Bayesian and E-Bayesian estimation for the unknown shape parameter of the Gumbel type-II distribution based on type-II censored samples. These estimators are obtained under symmetric loss function [squared error loss (SELF))] and various asymmetric loss functions [LINEX loss function (LLF), Degroot loss function (DLF), Quadratic loss function (QLF) and minimum expected loss function (MELF)]. Comparisons between the E-Bayesian estimators with the associated Bayesian estimators are investigated through a simulation study.</p>

APA, Harvard, Vancouver, ISO, and other styles

4

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 (April 3, 2016): 47. http://dx.doi.org/10.14419/ijasp.v4i1.5914.

Full text

Abstract:

<p>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.</p>

APA, Harvard, Vancouver, ISO, and other styles

5

Angali, Kambiz Ahmadi, S. Mahmoud Latifi, and David D. Hanagal. "Bayesian Estimation of Bivariate Exponential Distributions Based on Linex and Quadratic Loss Functions: A Survival Approach with Censored Samples." Communications in Statistics - Simulation and Computation 43, no. 1 (August 13, 2013): 31–44. http://dx.doi.org/10.1080/03610918.2012.697963.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Salem, Maram, Zeinab Amin, and Moshira Ismail. "Designing Bayesian Reliability Sampling Plans for Weibull Lifetime Models Using Progressively Censored Data." International Journal of Reliability, Quality and Safety Engineering 25, no. 03 (April 23, 2018): 1850012. http://dx.doi.org/10.1142/s0218539318500122.

Full text

Abstract:

This paper presents Bayesian reliability sampling plans for the Weibull distribution based on progressively Type-II censored data with binomial removals. In constructing sampling plans, the decision theoretic approach is used. A dependent bivariate nonconjugate prior is employed. The total cost of the sampling plan consists of sampling, time-consuming, rejection, and acceptance costs. The decision rule is based on the Bayes estimator of the survival function. Lindley’s approximation is used to obtain Bayes estimates of the survival function under the quadratic and LINEX loss functions. However, the poor performance of Lindley’s approximation with small sample sizes can be observed. The Metropolis-within-Gibbs Markov Chain Monte Carlo (MCMC) algorithm show significantly improved performance compared to Lindley’s approximation. We use simulation studies to evaluate the Bayes risk and determine the optimal sampling plans for different sample sizes, observed number of failures, binomial removal probabilities and minimum acceptable reliability.

APA, Harvard, Vancouver, ISO, and other styles

7

Cairns, Andrew. "Some Notes on the Dynamics and Optimal Control of Stochastic Pension Fund Models in Continuous Time." ASTIN Bulletin 30, no. 1 (May 2000): 19–55. http://dx.doi.org/10.2143/ast.30.1.504625.

Full text

Abstract:

AbstractThis paper discusses the modelling and control of pension funds.A continuous-time stochastic pension fund model is proposed in which there are n risky assets plus the risk-free asset as well as randomness in the level of benefit outgo. We consider Markov control strategies which optimise over the contribution rate and over the range of possible asset-allocation strategies.For a general (not necessarily quadratic) loss function it is shown that the optimal proportions of the fund invested in each of the risky assets remain constant relative to one another. Furthermore, the asset allocation strategy always lies on the capital market line familiar from modern portfolio theory.A general quadratic loss function is proposed which provides an explicit solution for the optimal contribution and asset-allocation strategies. It is noted that these solutions are not dependent on the level of uncertainty in the level of benefit outgo, suggesting that small schemes should operate in the same way as large ones. The optimal asset-allocation strategy, however, is found to be counterintuitive leading to some discussion of the form of the loss function. Power and exponential loss functions are then investigated and related problems discussed.The stationary distribution of the process is considered and optimal strategies compared with dynamic control strategies.Finally there is some discussion of the effects of constraints on contribution and asset-allocation strategies.

APA, Harvard, Vancouver, ISO, and other styles

8

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 (February 29, 2020): 38. http://dx.doi.org/10.5539/ijsp.v9n2p38.

Full text

Abstract:

This paper develops a Bayesian analysis of the scale parameter in the Weibull distribution with a scale parameter  θ  and shape parameter  β (known). For the prior distribution of the parameter involved, inverted Gamma distribution has been examined. Bayes estimates of the scale parameter, θ  , 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.

APA, Harvard, Vancouver, ISO, and other styles

9

Al-Duais, Fuad S. "Bayesian Analysis of Record Statistic from the Inverse Weibull Distribution under Balanced Loss Function." Mathematical Problems in Engineering 2021 (March 25, 2021): 1–9. http://dx.doi.org/10.1155/2021/6648462.

Full text

Abstract:

The main contribution of this work is to develop a linear exponential loss function (LINEX) to estimate the scale parameter and reliability function of the inverse Weibull distribution (IWD) based on lower record values. We do this by merging a weight into LINEX to produce a new loss function called weighted linear exponential loss function (WLINEX). We then use WLINEX to derive the scale parameter and reliability function of the IWD. Subsequently, we discuss the balanced loss functions for three different types of loss function, which include squared error (SE), LINEX, and WLINEX. The majority of previous scholars determined the weighted balanced coefficients without mathematical justification. One of the main contributions of this work is to utilize nonlinear programming to obtain the optimal values of the weighted coefficients for balanced squared error (BSE), balanced linear exponential (BLINEX), and balanced weighted linear exponential (BWLINEX) loss functions. Furthermore, to examine the performance of the proposed methods—WLINEX and BWLINEX—we conduct a Monte Carlo simulation. The comparison is between the proposed methods and other methods including maximum likelihood estimation, SE loss function, LINEX, BSE, and BLINEX. The results of simulation show that the proposed models BWLINEX and WLINEX in this work have the best performance in estimating scale parameter and reliability, respectively, according to the smallest values of mean SE. This result means that the proposed approach is promising and can be applied in a real environment.

APA, Harvard, Vancouver, ISO, and other styles

10

Kaur, Kamaljit, Sangeeta Arora, and Kalpana K. Mahajan. "Bayesian Estimation of Inequality and Poverty Indices in Case of Pareto Distribution Using Different Priors under LINEX Loss Function." Advances in Statistics 2015 (January 29, 2015): 1–10. http://dx.doi.org/10.1155/2015/964824.

Full text

Abstract:

Bayesian estimators of Gini index and a Poverty measure are obtained in case of Pareto distribution under censored and complete setup. The said estimators are obtained using two noninformative priors, namely, uniform prior and Jeffreys’ prior, and one conjugate prior under the assumption of Linear Exponential (LINEX) loss function. Using simulation techniques, the relative efficiency of proposed estimators using different priors and loss functions is obtained. The performances of the proposed estimators have been compared on the basis of their simulated risks obtained under LINEX loss function.

APA, Harvard, Vancouver, ISO, and other styles

11

Chang, Yen-chang, and Wen-liang Hung. "LINEX Loss Functions with Applications to Determining the Optimum Process Parameters." Quality & Quantity 41, no. 2 (January 23, 2007): 291–301. http://dx.doi.org/10.1007/s11135-005-5425-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Zhou, Hui. "Data Processing with Computation in Bayes Reliability Analysis for Burr Type X Distribution under Different Loss Functions." Advanced Materials Research 978 (June 2014): 205–8. http://dx.doi.org/10.4028/www.scientific.net/amr.978.205.

Full text

Abstract:

This paper studies the estimation of the parameter of Burr Type X distribution. Maximum likelihood estimator is first derived, and then the Bayes and Empirical Bayes estimators of the unknown parameter are obtained under three loss functions, which are squared error loss, LINEX loss and entropy loss functions. The prior distribution of parmeter used in this paper is Gamma distribution. Finally, a Monte Carlo simulation is given to illustrate the application of these estimators.

APA, Harvard, Vancouver, ISO, and other styles

13

Lan, Hai Ying. "Empirical Bayes Estimation of Parameter of Burr-Type X Model under LINEX and Squared Error Loss Functions." Advanced Materials Research 403-408 (November 2011): 5273–77. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.5273.

Full text

Abstract:

The Empirical Bayes estimate of the parameter of Burr-type X distribution is contained .The estimate is obtained under squared error loss and Varian’s linear-exponential (LINEX) loss functions, and is compared with corresponding maximum likelihood and Bayes estimates. Finally, a Monte Carlo numerical example is given to illustrate our results.

APA, Harvard, Vancouver, ISO, and other styles

14

Mohammed Ahmed, Dr Al Omari. "Bayesian Methods and Maximum Likelihood Estimations of Exponential Censored Time Distribution with Cure Fraction." Academic Journal of Applied Mathematical Sciences, no. 72 (March 6, 2021): 106–12. http://dx.doi.org/10.32861/ajams.72.106.112.

Full text

Abstract:

This paper is focused on estimating the parameter of Exponential distribution under right-censored data with cure fraction. The maximum likelihood estimation and Bayesian approach were used. The Bayesian method is implemented using gamma, Jeffreys, and extension of Jeffreys priors with two loss functions, which are; squared error loss function and Linear Exponential Loss Function (LINEX). The methods of the Bayesian approach are compared to maximum likelihood counterparts and the comparisons are made with respect to the Mean Square Error (MSE) to determine the best for estimating the parameter of Exponential distribution under right-censored data with cure fraction. The results show that the Bayesian with gamma prior under LINEX loss function is a better estimation of the parameter of Exponential distribution with cure fraction based on right-censored data.

APA, Harvard, Vancouver, ISO, and other styles

15

Hassan, N. J., J. Mahdi Hadad, and A. Hawad Nasar. "Bayesian Shrinkage Estimator of Burr XII Distribution." International Journal of Mathematics and Mathematical Sciences 2020 (June 22, 2020): 1–6. http://dx.doi.org/10.1155/2020/7953098.

Full text

Abstract:

In this paper, we derive the generalized Bayesian shrinkage estimator of parameter of Burr XII distribution under three loss functions: squared error, LINEX, and weighted balance loss functions. Therefore, we obtain three generalized Bayesian shrinkage estimators (GBSEs). In this approach, we find the posterior risk function (PRF) of the generalized Bayesian shrinkage estimator (GBSE) with respect to each loss function. The constant formula of GBSE is computed by minimizing the PRF. In special cases, we derive two new GBSEs under the weighted loss function. Finally, we give our conclusion.

APA, Harvard, Vancouver, ISO, and other styles

16

Ali, Mohammed Jamel, Hazim Mansoor Gorgees, and Adel Abdul Kadhim Hussein. "The Comparison Between Standard Bayes Estimators of the Reliability Function of Exponential Distribution." Ibn AL- Haitham Journal For Pure and Applied Science 31, no. 3 (November 18, 2018): 135. http://dx.doi.org/10.30526/31.3.2006.

Full text

Abstract:

In this paper, a Monte Carlo Simulation technique is used to compare the performance of the standard Bayes estimators of the reliability function of the one parameter exponential distribution .Three types of loss functions are adopted, namely, squared error loss function (SELF) ,Precautionary error loss function (PELF) andlinear exponential error loss function(LINEX) with informative and non- informative prior .The criterion integrated mean square error (IMSE) is employed to assess the performance of such estimators

APA, Harvard, Vancouver, ISO, and other styles

17

Mahanta, J., and M. B. A. Talukdar. "A Bayesian Approach for Estimating Parameter of Rayleigh Distribution." Journal of Scientific Research 11, no. 1 (January 1, 2019): 23–39. http://dx.doi.org/10.3329/jsr.v11i1.37065.

Full text

Abstract:

This paper is concerned with estimating the parameter of Rayleigh distribution (special case of two parameters Weibull distribution) by adopting Bayesian approach under squared error (SE), LINEX, MLINEX loss function. The performances of the obtained estimators for different types of loss functions are then compared. Better result is found in Bayesian approach under MLINEX loss function. Bayes risk of the estimators are also computed and presented in graphs.

APA, Harvard, Vancouver, ISO, and other styles

18

Marti, K. "Stochastic structural optimisation with quadratic loss functions." Computers & Structures 88, no. 23-24 (December 2010): 1310–21. http://dx.doi.org/10.1016/j.compstruc.2008.12.010.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Shah, J. B., and M. N. Patel. "Bayes Estimation of a Two-Parameter Geometric Distribution under Multiply Type II Censoring." International Journal of Quality, Statistics, and Reliability 2011 (May 11, 2011): 1–10. http://dx.doi.org/10.1155/2011/618347.

Full text

Abstract:

We derive Bayes estimators of reliability and the parameters of a two- parameter geometric distribution under the general entropy loss, minimum expected loss and linex loss, functions for a noninformative as well as beta prior from multiply Type II censored data. We have studied the robustness of the estimators using simulation and we observed that the Bayes estimators of reliability and the parameters of a two-parameter geometric distribution under all the above loss functions appear to be robust with respect to the correct choice of the hyperparameters a(b) and a wrong choice of the prior parameters b(a) of the beta prior.

APA, Harvard, Vancouver, ISO, and other styles

20

Almazah, Mohammed Mohammed Ahmed. "Estimation of the Parameters for the Exponentiated Weibull Distribution Based on Progressive Type-II Censoring Scheme." International Journal of Statistics and Probability 9, no. 5 (July 28, 2020): 1. http://dx.doi.org/10.5539/ijsp.v9n5p1.

Full text

Abstract:

The main objective of the present study is to find the estimation of the two Exponentiated Weibull distribution parameters, based on progressive Type II censored samples. The maximum likelihood and Bayes estimators for the two shape parameters and the scale parameter of the exponentiated Weibull lifetime model were derived. Bayes estimators was obtained by using both the symmetric and asymmetric loss functions via squared error loss and linex loss functions This was done with respect to the conjugate priors for two shape parameters. We used an approximation based on the Lindley (Trabajos de Estadistca) method for obtaining Bayes estimates under these loss functions. The different proposed estimators have been compared through an extensive simulation studies. Bayes ratings also turned out to be better than MLE. Whatever the sample sizes are, we get the same results.

APA, Harvard, Vancouver, ISO, and other styles

21

Pandya, Mayuri, Krishnam Bhatt, and Paresh Andharia. "Bayes Estimation of Two-Phase Linear Regression Model." International Journal of Quality, Statistics, and Reliability 2011 (July 26, 2011): 1–9. http://dx.doi.org/10.1155/2011/357814.

Full text

Abstract:

Let the regression model be Yi=β1Xi+εi, where εi are i. i. d. N (0,σ2) random errors with variance σ2>0 but later it was found that there was a change in the system at some point of time m and it is reflected in the sequence after Xm by change in slope, regression parameter β2. The problem of study is when and where this change has started occurring. This is called change point inference problem. The estimators of m, β1,β2 are derived under asymmetric loss functions, namely, Linex loss & General Entropy loss functions. The effects of correct and wrong prior information on the Bayes estimates are studied.

APA, Harvard, Vancouver, ISO, and other styles

22

Panwar, M. S., and Sanjeev K. Tomer. "Robust Bayesian Analysis of Lifetime Data from Maxwell Distribution." Austrian Journal of Statistics 48, no. 1 (December 17, 2018): 38–55. http://dx.doi.org/10.17713/ajs.v47i4.692.

Full text

Abstract:

In this paper, we consider robust Bayesian analysis of lifetime data from the Maxwell distribution assuming an $\varepsilon$-contamination class of prior distributions for the parameter. We obtain robust Bayes estimates of the parameter and mean lifetime under squared error and LINEX loss functions in presence of uncensored as well as Type-I progressively hybrid censored lifetime data. A real data set is analysed for numerical illustrations.

APA, Harvard, Vancouver, ISO, and other styles

23

Khan, Nida, and Muhammad Aslam. "Statistical Analysis of Location Parameter of Inverse Gaussian Distribution Under Noninformative Priors." Journal of Quantitative Methods 3, no. 2 (August 31, 2019): 62–76. http://dx.doi.org/10.29145/2019/jqm/030204.

Full text

Abstract:

Bayesian estimation for location parameter of the inverse Gaussian distribution is presented in this paper. Noninformative priors (Uniform and Jeffreys) are assumed to be the prior distributions for the location parameter as the shape parameter of the distribution is considered to be known. Four loss functions: Squared error, Trigonometric, Squared logarithmic and Linex are used for estimation. Bayes risks are obtained to find the best Bayes estimator through simulation study and real life data

APA, Harvard, Vancouver, ISO, and other styles

24

Shi, Xiao Lin. "Reliability Analysis for the Burr XII Units under Random Censoring." Applied Mechanics and Materials 321-324 (June 2013): 2265–68. http://dx.doi.org/10.4028/www.scientific.net/amm.321-324.2265.

Full text

Abstract:

Based on random censored samples, the problem of estimating unknown parameters and reliability performances of the two-parameter Burr type XII units is considered. Firstly, we obtained the Bayesian estimates of the parameter for the two-parameter Burr type XII distribution under the asymmetric Linex loss functions. Secondly, the Bayesian estimates of the reliability performances are derived. In order to investigate the accuracy of estimations, an illustrative example is examined numerically by the Monte-Carlo simulation.

APA, Harvard, Vancouver, ISO, and other styles

25

Al-Duais, Fuad S., and Mohammed Alhagyan. "Nonlinear Programming to Determine Best Weighted Coefficient of Balanced LINEX Loss Function Based on Lower Record Values." Complexity 2021 (June 1, 2021): 1–6. http://dx.doi.org/10.1155/2021/5273191.

Full text

Abstract:

Majority research studies in the literature determine the weighted coefficients of balanced loss function by suggesting some arbitrary values and then conducting comparison study to choose the best. However, this methodology is not efficient because there is no guarantee ensures that one of the chosen values is the best. This encouraged us to look for mathematical method that gives and guarantees the best values of the weighted coefficients. The proposed methodology in this research is to employ the nonlinear programming in determining the weighted coefficients of balanced loss function instead of the unguaranteed old methods. In this research, we consider two balanced loss functions including balanced square error (BSE) loss function and balanced linear exponential (BLINEX) loss function to estimate the parameter and reliability function of inverse Rayleigh distribution (IRD) based on lower record values. Comparisons are made between Bayesian estimators (SE, BSE, LINEX, and BLINEX) and maximum likelihood estimator via Monte Carlo simulation. The evaluation was done based on absolute bias and mean square errors. The outputs of the simulation showed that the balanced linear exponential (BLINEX) loss function has the best performance. Moreover, the simulation verified that the balanced loss functions are always better than corresponding loss function.

APA, Harvard, Vancouver, ISO, and other styles

26

MOHAN, RAKHI, and MANOJ CHACKO. "Statistical inference for Kumaraswamy-exponential distribution based on progressive Type-II censored data with binomial removals." Journal of Statistical Research 53, no. 2 (March 1, 2020): 147–63. http://dx.doi.org/10.47302/jsr.2019530204.

Full text

Abstract:

In this paper, estimation of parameters of Kumaraswamy-exponential distribution with shape parameters α and β is considered based on a progressively type-II censored sample with binomial removals. Together with the unknown parameters, the removal probability p is also estimated. Bayes estimators are obtained using different loss functions such as squared error, LINEX loss function and entropy loss function. All Bayesian estimates are compared with the corresponding maximum likelihood estimates numerically in terms of their bias and mean square error values and found that Bayes estimators perform better than MLE’s for β and p and MLEs perform better than Bayes estimators for α. A real data set is also used for illustration.

APA, Harvard, Vancouver, ISO, and other styles

27

Choi, Hoo-Gon R., Man-Hee Park, and Erik Salisbury. "Optimal Tolerance Allocation With Loss Functions." Journal of Manufacturing Science and Engineering 122, no. 3 (September 1, 1999): 529–35. http://dx.doi.org/10.1115/1.1285918.

Full text

Abstract:

The tolerance allocation problem is formulated as a nonlinear integer model under the constraints of process capability. The problem is to minimize the sum of machining cost and quality loss. When the statistical tolerance limits are used and Taguchi’s quadratic loss function is defined, the total cost function becomes a convex function for a given feature and process. A complex search method is used to solve the model and ensure the optimal tolerance allocation. Numerical examples are presented demonstrating successful model implementation for both linear and nonlinear design functions. [S1087-1357(00)02602-2]

APA, Harvard, Vancouver, ISO, and other styles

28

Boratyńska, Agata. "Posterior Regret Γ-Minimax Estimation of Insurance Premium in Collective Risk Model." ASTIN Bulletin 38, no. 01 (May 2008): 277–91. http://dx.doi.org/10.2143/ast.38.1.2030414.

Full text

Abstract:

The collective risk model for the insurance claims is considered. The objective is to estimate a premium which is defined as a functional H specified up to an unknown parameter θ (the expected number of claims). Four principles of calculating a premium are applied. The Bayesian methodology, which combines the prior knowledge about a parameter θ with the knowledge in the form of a random sample is adopted. Two loss functions (the square-error loss function and the asymmetric loss function LINEX) are considered. Some uncertainty about a prior is assumed by introducing classes of priors. Considering one of the concepts of robust procedures the posterior regret Γ-minimax premiums are calculated, as an optimal robust premiums. A numerical example is presented.

APA, Harvard, Vancouver, ISO, and other styles

29

Boratyńska, Agata. "Posterior Regret Γ-Minimax Estimation of Insurance Premium in Collective Risk Model." ASTIN Bulletin 38, no. 1 (May 2008): 277–91. http://dx.doi.org/10.1017/s0515036100015178.

Full text

Abstract:

The collective risk model for the insurance claims is considered. The objective is to estimate a premium which is defined as a functional H specified up to an unknown parameter θ (the expected number of claims). Four principles of calculating a premium are applied. The Bayesian methodology, which combines the prior knowledge about a parameter θ with the knowledge in the form of a random sample is adopted. Two loss functions (the square-error loss function and the asymmetric loss function LINEX) are considered. Some uncertainty about a prior is assumed by introducing classes of priors. Considering one of the concepts of robust procedures the posterior regret Γ-minimax premiums are calculated, as an optimal robust premiums. A numerical example is presented.

APA, Harvard, Vancouver, ISO, and other styles

30

Noor, Farzana, Saadia Masood, Mehwish Zaman, Maryam Siddiqa, Raja Asif Wagan, Imran Ullah Khan, and Ahthasham Sajid. "Bayesian Analysis of Inverted Kumaraswamy Mixture Model with Application to Burning Velocity of Chemicals." Mathematical Problems in Engineering 2021 (May 18, 2021): 1–18. http://dx.doi.org/10.1155/2021/5569652.

Full text

Abstract:

Burning velocity of different chemicals is estimated using a model from mixed population considering inverted Kumaraswamy (IKum) distribution for component parts. Two estimation techniques maximum likelihood estimation (MLE) and Bayesian analysis are applied for estimation purposes. BEs of a mixture model are obtained using gamma, inverse beta prior, and uniform prior distribution with two loss functions. Hyperparameters are determined through the empirical Bayesian method. An extensive simulation study is also a part of the study which is used to foresee the characteristics of the presented model. Application of the IKum mixture model is presented through a real dataset. We observed from the results that Linex loss performed better than squared error loss as it resulted in lower risks. And similarly gamma prior is preferred over other priors.

APA, Harvard, Vancouver, ISO, and other styles

31

Murat, Małgorzata. "Bayesian estimation for non zero inflated modified power series distribution under linex and generalized entropy loss functions." Communications in Statistics - Theory and Methods 45, no. 13 (October 26, 2015): 3952–69. http://dx.doi.org/10.1080/03610926.2014.912057.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Liu, Shuhan, and Wenhao Gui. "Estimating the Entropy for Lomax Distribution Based on Generalized Progressively Hybrid Censoring." Symmetry 11, no. 10 (October 1, 2019): 1219. http://dx.doi.org/10.3390/sym11101219.

Full text

Abstract:

As it is often unavoidable to obtain incomplete data in life testing and survival analysis, research on censoring data is becoming increasingly popular. In this paper, the problem of estimating the entropy of a two-parameter Lomax distribution based on generalized progressively hybrid censoring is considered. The maximum likelihood estimators of the unknown parameters are derived to estimate the entropy. Further, Bayesian estimates are computed under symmetric and asymmetric loss functions, including squared error, linex, and general entropy loss function. As we cannot obtain analytical Bayesian estimates directly, the Lindley method and the Tierney and Kadane method are applied. A simulation study is conducted and a real data set is analyzed for illustrative purposes.

APA, Harvard, Vancouver, ISO, and other styles

33

Eissa, Fathy Helmy. "Stress-Strength Reliability Model with The Exponentiated Weibull Distribution: Inferences and Applications." International Journal of Statistics and Probability 7, no. 4 (June 25, 2018): 78. http://dx.doi.org/10.5539/ijsp.v7n4p78.

Full text

Abstract:

In this paper, we deal with the estimation of the reliability $R=P(Y<X)$ where $X$, a unit strength, and $Y$, a unit stress, are independent exponentiated Weibull random variables. The maximum likelihood and Bayesian methods are used to make inference about $R$. We obtain the Baysian estimator using Lindely's procedure under squared error loss and LINEX loss functions with gamma prior for the unknown model parameters. The asymptotic and bootstrap confidence intervals are obtained as well as the credible interval for R is constructed in view of the empirical Bayesian procedure. For illustrative purposes, analysis of real data sets is presented. Mont Carlo simulations are carried out to compare the performances of the different estimators.

APA, Harvard, Vancouver, ISO, and other styles

34

Singh, Shane. "Linear and quadratic utility loss functions in voting behavior research." Journal of Theoretical Politics 26, no. 1 (July 18, 2013): 35–58. http://dx.doi.org/10.1177/0951629813488985.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

Zeng, Xinyi, and Wenhao Gui. "Statistical Inference of Truncated Normal Distribution Based on the Generalized Progressive Hybrid Censoring." Entropy 23, no. 2 (February 2, 2021): 186. http://dx.doi.org/10.3390/e23020186.

Full text

Abstract:

In this paper, the parameter estimation problem of a truncated normal distribution is discussed based on the generalized progressive hybrid censored data. The desired maximum likelihood estimates of unknown quantities are firstly derived through the Newton–Raphson algorithm and the expectation maximization algorithm. Based on the asymptotic normality of the maximum likelihood estimators, we develop the asymptotic confidence intervals. The percentile bootstrap method is also employed in the case of the small sample size. Further, the Bayes estimates are evaluated under various loss functions like squared error, general entropy, and linex loss functions. Tierney and Kadane approximation, as well as the importance sampling approach, is applied to obtain the Bayesian estimates under proper prior distributions. The associated Bayesian credible intervals are constructed in the meantime. Extensive numerical simulations are implemented to compare the performance of different estimation methods. Finally, an authentic example is analyzed to illustrate the inference approaches.

APA, Harvard, Vancouver, ISO, and other styles

36

Badr, M. M. "Estimations and Prediction for the Compound Rayleigh Distribution Based on Upper Record Values." Journal of Computational and Theoretical Nanoscience 15, no. 2 (February 1, 2018): 711–18. http://dx.doi.org/10.1166/jctn.2018.7149.

Full text

Abstract:

This article considers estimation of the unknown parameters for the compound Rayleigh distribution (CRD) based on upper record values. We have derived the maximum likelihood (ML) and Bayesian estimators for the unknown two parameters, as well as the reliability and hazard functions. We obtained Bayes estimators on the basis of the symmetric (squared error) and asymmetric (linear exponential (LINEX) and general entropy (GE)) loss functions. It has been seen that the symmetric and asymmetric Bayes estimators are obtained in closed forms. Furthermore, Bayesian prediction interval of the future upper record values are discussed and obtained. Finally, estimation of the parameters, practical examples of real record values and simulated record values are given to illustrate the theoretical results of prediction interval.

APA, Harvard, Vancouver, ISO, and other styles

37

Cho, Byung-Rae, and Michael S. Leonard. "Identification and Extensions of Quasiconvex Quality Loss Functions." International Journal of Reliability, Quality and Safety Engineering 04, no. 02 (June 1997): 191–204. http://dx.doi.org/10.1142/s0218539397000138.

Full text

Abstract:

This paper presents a set of related quasiconvex quality loss functions. Characteristics of quasiconvex functions that are desirable for modeling quality loss are noted. Three frequently used univariate quasiconvex quality loss functions are discussed. Bivariate and multivariate quasiconvex quality loss functions are developed. A set of necessary and sufficient conditions is established for the quasiconvexity of multivariate quality loss functions. An industrial product example is used to illustrate the development of a bivariate quadratic quality loss function.

APA, Harvard, Vancouver, ISO, and other styles

38

Krishna, Hare, and Neha Goel. "Maximum Likelihood and Bayes Estimation in Randomly Censored Geometric Distribution." Journal of Probability and Statistics 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/4860167.

Full text

Abstract:

In this article, we study the geometric distribution under randomly censored data. Maximum likelihood estimators and confidence intervals based on Fisher information matrix are derived for the unknown parameters with randomly censored data. Bayes estimators are also developed using beta priors under generalized entropy and LINEX loss functions. Also, Bayesian credible and highest posterior density (HPD) credible intervals are obtained for the parameters. Expected time on test and reliability characteristics are also analyzed in this article. To compare various estimates developed in the article, a Monte Carlo simulation study is carried out. Finally, for illustration purpose, a randomly censored real data set is discussed.

APA, Harvard, Vancouver, ISO, and other styles

39

Zhang, Fengshi, and Wenhao Gui. "Parameter and Reliability Inferences of Inverted Exponentiated Half-Logistic Distribution under the Progressive First-Failure Censoring." Mathematics 8, no. 5 (May 3, 2020): 708. http://dx.doi.org/10.3390/math8050708.

Full text

Abstract:

Using progressive first-failure censored samples, we mainly study the inferences of the unknown parameters and the reliability and failure functions of the Inverted Exponentiated Half-Logistic distribution. The progressive first-failure censoring is an extension and improvement of progressive censoring, which is of great significance in the field of lifetime research. Besides maximum likelihood estimation, we use Bayesian estimation under unbalanced and balanced losses: General Entropy loss function, Squared Error loss function and Linex loss function. Approximate explicit expression of Bayesian estimation is given using Lindley approximation method for point estimation and Metropolis-Hastings method for point and interval estimation. Bayesian credible intervals and asymptotic confidence intervals are derived in the form of average length and coverage probability. To show the research effects, a simulation study and practical data analysis are carried out. Finally, we discuss the optimal censoring mode under four different criteria.

APA, Harvard, Vancouver, ISO, and other styles

40

Tu, Jiayi, and Wenhao Gui. "Bayesian Inference for the Kumaraswamy Distribution under Generalized Progressive Hybrid Censoring." Entropy 22, no. 9 (September 15, 2020): 1032. http://dx.doi.org/10.3390/e22091032.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

41

Okasha, Hassan, and Abdelfattah Mustafa. "E-Bayesian Estimation for the Weibull Distribution under Adaptive Type-I Progressive Hybrid Censored Competing Risks Data." Entropy 22, no. 8 (August 17, 2020): 903. http://dx.doi.org/10.3390/e22080903.

Full text

Abstract:

This article focuses on using E-Bayesian estimation for the Weibull distribution based on adaptive type-I progressive hybrid censored competing risks (AT-I PHCS). The case of Weibull distribution for the underlying lifetimes is considered assuming a cumulative exposure model. The E-Bayesian estimation is discussed by considering three different prior distributions for the hyper-parameters. The E-Bayesian estimators as well as the corresponding E-mean square errors are obtained by using squared and LINEX loss functions. Some properties of the E-Bayesian estimators are also derived. A simulation study to compare the various estimators and real data application is applied to show the applicability of the different estimators are proposed.

APA, Harvard, Vancouver, ISO, and other styles

42

Zhang, Yuxuan, Kaiwei Liu, and Wenhao Gui. "Bayesian and E-Bayesian Estimations of Bathtub-Shaped Distribution under Generalized Type-I Hybrid Censoring." Entropy 23, no. 8 (July 22, 2021): 934. http://dx.doi.org/10.3390/e23080934.

Full text

Abstract:

For the purpose of improving the statistical efficiency of estimators in life-testing experiments, generalized Type-I hybrid censoring has lately been implemented by guaranteeing that experiments only terminate after a certain number of failures appear. With the wide applications of bathtub-shaped distribution in engineering areas and the recently introduced generalized Type-I hybrid censoring scheme, considering that there is no work coalescing this certain type of censoring model with a bathtub-shaped distribution, we consider the parameter inference under generalized Type-I hybrid censoring. First, estimations of the unknown scale parameter and the reliability function are obtained under the Bayesian method based on LINEX and squared error loss functions with a conjugate gamma prior. The comparison of estimations under the E-Bayesian method for different prior distributions and loss functions is analyzed. Additionally, Bayesian and E-Bayesian estimations with two unknown parameters are introduced. Furthermore, to verify the robustness of the estimations above, the Monte Carlo method is introduced for the simulation study. Finally, the application of the discussed inference in practice is illustrated by analyzing a real data set.

APA, Harvard, Vancouver, ISO, and other styles

43

Lin, Shao-Bo, Jinshan Zeng, and Xiangyu Chang. "Learning Rates for Classification with Gaussian Kernels." Neural Computation 29, no. 12 (December 2017): 3353–80. http://dx.doi.org/10.1162/neco_a_00968.

Full text

Abstract:

This letter aims at refined error analysis for binary classification using support vector machine (SVM) with gaussian kernel and convex loss. Our first result shows that for some loss functions, such as the truncated quadratic loss and quadratic loss, SVM with gaussian kernel can reach the almost optimal learning rate provided the regression function is smooth. Our second result shows that for a large number of loss functions, under some Tsybakov noise assumption, if the regression function is infinitely smooth, then SVM with gaussian kernel can achieve the learning rate of order [Formula: see text], where [Formula: see text] is the number of samples.

APA, Harvard, Vancouver, ISO, and other styles

44

Jin, Qiu, and Shao Gang Liu. "Research of Asymmetric Quality Loss Function with Triangular Distribution." Advanced Materials Research 655-657 (January 2013): 2331–34. http://dx.doi.org/10.4028/www.scientific.net/amr.655-657.2331.

Full text

Abstract:

The asymmetric quality loss functions with the triangular distribution for determining the optimum process mean are studied. The condition of using the linear and quadratic asymmetric quality loss function in the model is considered. The eight mathematical models under an asymmetric quality loss function with the triangular distribution based on the analysis of the linear and quadratic asymmetric quality loss function are presented. Finally, the validity of models is verified by the examples.

APA, Harvard, Vancouver, ISO, and other styles

45

Alotaibi, Refah, Mervat Khalifa, Lamya A. Baharith, Sanku Dey, and H. Rezk. "The Mixture of the Marshall–Olkin Extended Weibull Distribution under Type-II Censoring and Different Loss Functions." Mathematical Problems in Engineering 2021 (May 18, 2021): 1–15. http://dx.doi.org/10.1155/2021/6654101.

Full text

Abstract:

To study the heterogeneous nature of lifetimes of certain mechanical or engineering processes, a mixture model of some suitable lifetime distributions may be more appropriate and appealing as compared to simple models. This paper considers a mixture of the Marshall–Olkin extended Weibull distribution for efficient modeling of failure, survival, and COVID-19 data under classical and Bayesian perspectives based on type-II censored data. We derive several properties of the new distribution such as moments, incomplete moments, mean deviation, average lifetime, mean residual lifetime, Rényi entropy, Shannon entropy, and order statistics of the proposed distribution. Maximum likelihood and Bayes procedure are used to derive both point and interval estimates of the parameters involved in the model. Bayes estimators of the unknown parameters of the model are obtained under symmetric (squared error) and asymmetric (linear exponential (LINEX)) loss functions using gamma priors for both the shape and the scale parameters. Furthermore, approximate confidence intervals and Bayes credible intervals (CIs) are also obtained. Monte Carlo simulation study is carried out to assess the performance of the maximum likelihood estimators and Bayes estimators with respect to their estimated risk. The flexibility and importance of the proposed distribution are illustrated by means of four real datasets.

APA, Harvard, Vancouver, ISO, and other styles

46

Jia, Jun-Mei, Zai-Zai Yan, and Xiu-Yun Peng. "Estimation for inverse Gaussian distribution under first-failure progressive hybird censored samples." Filomat 31, no. 18 (2017): 5743–52. http://dx.doi.org/10.2298/fil1718743j.

Full text

Abstract:

In this paper, a first-failure progressive hybird censoring scheme is introduced that combines progressive first-failure censoring and Type-I censoring. We obtain the maximum likelihood estimators (MLEs) and the Bayes estimators of the unknown parameters from the inverse Gaussian distribution based on the first-failure progressive hybird censoring scheme. The Bayes estimates are computed under squared error, Linex and general entropy loss functions. The asymptotic confidence intervals and coverage probabilities for the parameters are obtained based on the observed Fisher?s information matrix. Also, highest posterior density credible intervals for the parameters are computed using Gibbs sampling procedure. A Monte Carlo simulation study is conducted in order to compare the Bayes estimators with the MLEs. Real life data sets are provided to illustration purposes.

APA, Harvard, Vancouver, ISO, and other styles

47

Maghsoodloo, Saeed, and Chun-Lang Chang. "Quadratic loss functions and signal-to-noise ratios for a bivariate response." Journal of Manufacturing Systems 20, no. 1 (January 2001): 1–12. http://dx.doi.org/10.1016/s0278-6125(01)80015-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

Liu, Kaiwei, and Yuxuan Zhang. "The E-Bayesian Estimation for Lomax Distribution Based on Generalized Type-I Hybrid Censoring Scheme." Mathematical Problems in Engineering 2021 (May 19, 2021): 1–19. http://dx.doi.org/10.1155/2021/5570320.

Full text

Abstract:

This article studies the E-Bayesian estimation of the unknown parameter of Lomax distribution based on generalized Type-I hybrid censoring. Under square error loss and LINEX loss functions, we get the E-Bayesian estimation and compare its effectiveness with Bayesian estimation. To measure the error of E-Bayesian estimation, the expectation of mean square error (E-MSE) is introduced. With Markov chain Monte Carlo technology, E-Bayesian estimations are computed. Metropolis–Hastings algorithm is applied within the process. Similarly, the credible interval for the parameter is calculated. Then, we can compare the MSE and E-MSE to evaluate whose result is more effective. For the purpose of illustration in real datasets, cases of generalized Type-I hybrid censored samples are presented. In order to judge whether the sample data can be directly fitted by the Lomax distribution, we adopt the Kolmogorov–Smirnov tests for evaluation. Finally, we can get the conclusion after comparing the results of E-Bayesian and Bayesian estimation.

APA, Harvard, Vancouver, ISO, and other styles

49

Cai, Yuxin, and Wenhao Gui. "Classical and Bayesian Inference for a Progressive First-Failure Censored Left-Truncated Normal Distribution." Symmetry 13, no. 3 (March 16, 2021): 490. http://dx.doi.org/10.3390/sym13030490.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

50

Rabie, Abdalla, and Junping Li. "E-Bayesian Estimation Based on Burr-X Generalized Type-II Hybrid Censored Data." Symmetry 11, no. 5 (May 3, 2019): 626. http://dx.doi.org/10.3390/sym11050626.

Full text

Abstract:

In this article, we are concerned with the E-Bayesian (the expectation of Bayesian estimate) method, the maximum likelihood and the Bayesian estimation methods of the shape parameter, and the reliability function of one-parameter Burr-X distribution. A hybrid generalized Type-II censored sample from one-parameter Burr-X distribution is considered. The Bayesian and E-Bayesian approaches are studied under squared error and LINEX loss functions by using the Markov chain Monte Carlo method. Confidence intervals for maximum likelihood estimates, as well as credible intervals for the E-Bayesian and Bayesian estimates, are constructed. Furthermore, an example of real-life data is presented for the sake of the illustration. Finally, the performance of the E-Bayesian estimation method is studied then compared with the performance of the Bayesian and maximum likelihood methods.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!