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Journal articles on the topic 'Burr type XII distribution'

Author: Grafiati

Published: 3 June 2025

Last updated: 13 July 2025

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1

Al-Khazaleh, Ahmad M. H. "Transmuted Burr type XII distribution: a generalization of the Burr type XII distribution." International Mathematical Forum 11 (2016): 547–56. http://dx.doi.org/10.12988/imf.2016.6443.

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2

fawzy, hala, and hala fawzy. "Extended Burr Type XII Distribution." Egyptian Statistical Journal 66, no. 2 (2022): 17–41. http://dx.doi.org/10.21608/esju.2023.183619.1009.

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3

Ilikkan, Eda Selin, and Elif Yildirim. "The Type I Half Logistic-Burr XII lifetime distribution : Properties and application to survival data." Journal of Statistics and Management Systems 27, no. 5 (2024): 835–52. http://dx.doi.org/10.47974/jsms-934.

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Real life data cannot fit to the commonly known statistical model structures and therefore, different new models are needed in the modeling of this type of data. In this paper, we propose a new lifetime distribution called the Type I Half Logistic-Burr XII that can model different data from engineering and biomedicine science with its flexible structure. For this new distribution, we obtain the statistical properties including the hazard function, survival function, moment generating function, variance, quantile function, skewness and kurtosis. Moreover, the unknown parameters of the proposed type I half logistic-Burr XII distribution are obtained by using the maximum likelihood method. Application with two survival time data is presented to illustrate the effectiveness of the new distributions and it is shown to be better than the Burr XII, Topp-Leone Burr XII and Extended Weibull Log-Logistic distribution.

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4

Para, B. A., and T. R. Jan. "Discrete Generalized Burr-Type XII Distribution." Journal of Modern Applied Statistical Methods 13, no. 2 (2014): 244–58. http://dx.doi.org/10.22237/jmasm/1414815120.

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5

Khalil, Mohamed G., Khaoula Aidi, M. Masoom Ali, Nadeem S. Butt, Mohamed Ibrahim, and Haitham M. Yousof. "Modified Bagdonavicius-Nikulin Goodness-of-fit Test Statistic for the Compound Topp Leone Burr XII Model with Various Censored Applications." Statistics, Optimization & Information Computing 12, no. 4 (2024): 851–68. http://dx.doi.org/10.19139/soic-2310-5070-1447.

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The Poisson Topp Leone Burr XII distribution is extensively studied due to its broad relevance in analyzing censored real datasets from engineering, economics, and medicine. In this research, the distribution's versatility is highlighted through the analysis of four specific real datasets. The study compares the Poisson Topp Leone Burr XII distribution with nine extensions of the Burr type XII distribution to determine which offers the best fit for these datasets. To evaluate the goodness-of-fit of the Poisson Topp Leone Burr XII distribution under right censoring, a modified Bagdonavi\v{c}ius-Nikulin goodness-of-fit test statistic is introduced and applied. This new test statistic is utilized to validate the distributional fit for the Poisson Topp Leone Burr XII distribution across the four right-censored datasets. The modified Bagdonavi\v{c}ius-Nikulin test statistic is employed to assess distributional validation, specifically in the context of right censoring. The application of this statistic involves analyzing each of the four censored datasets to confirm the appropriateness of the Poisson Topp Leone Burr XII distribution for these scenarios. Additionally, to support the evaluation of the modified goodness-of-fit test statistic, the Barzilai-Borwein algorithm is utilized. This algorithm is employed within a simulation study to further assess the effectiveness and reliability of the modified Bagdonavi\v{c}ius-Nikulin test statistic, thereby ensuring robust validation of the Poisson Topp Leone Burr XII distribution against the observed real datasets.

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6

Saxena, Suneet. "Software Reliability Growth Modeling Involving Burr Type XII distribution and Fault Removal Efficiency." SRMS Journal of Mathmetical Science 5, no. 01 (2019): 11–13. http://dx.doi.org/10.29218/srmsmaths.v5i1.2.

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In software reliability analysis various authors have used Burr type XII distribution to model the failure pattern of the system due to its wide variety of flexible shapes. In particular cases it can be reduced to Exponential, Normal, Weibull, Log-logistic, Gamma distributions etc. In proposed paper software reliability growth model has been developed incorporating fault removal efficiency (FRE) and Burr type XII based testing effort function. FRE represents fraction of detected faults which are removed completely. Parameters of model are predicted by LSE whereas MSE is used to perform comparison analysis. Results validate better fitting of data set.

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7

Saripalli, Arun Kumar, Sridhar Akiri, Rekha Sarode, B. V. Nagarjuna Vasili, and M. Ramanaiah. "Comparative Performance of Burr Type XII 3P, Dagum Type I 3P and Log-Logistic 3P Distributions in Modeling Ozone (O₃), PM₁₀ and PM₂.₅ Concentrations." Research Journal of Chemistry and Environment 29, no. 4 (2025): 39–56. https://doi.org/10.25303/294rjce039056.

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This study investigates the suitability of three parameters continuous probability distributions-Burr Type XII 3P, Dagum Type I 3P and Log-Logistic 3P-in modeling secondary air pollutants: ozone (O₃), particulate matters (PM₁₀ and PM₂.₅) in Visakhapatnam, an urban region having rapid industrialization. By employing rigorous statistical techniques including maximum likelihood estimation (MLE) and bootstrapping, we estimate distribution parameters and validate model fit through diagnostic plots-skewness vs. kurtosis, P-P and Q-Q plots as well as goodness-of-fit test-statistics, such as Kolmogorov-Smirnov(KS), Anderson-Darling(AD) and Cramér von Mises(CvM) tests. Additional, performance metrics including Akaike information criterion(AIC), Bayesian information criterion(BIC), evaluation metrics like mean absolute error(MAE), mean absolute percentage error(MAPE), mean squared error(MSE), root mean squared error(RMSE) and coefficient of determination(R²) and cross-validation, were also applied to ensure model robustness. Results indicate that the Burr Type XII 3P distribution most effectively models the high variability and skewed nature of O₃ concentrations, while the Dagum Type I 3P distribution provides the best fit for PM₁₀ and both Burr Type XII 3P and Log-Logistic 3P distributions are suitable for PM₂.₅. These findings offer new insights into the behavior of secondary pollutants, supporting the development of robust air quality monitoring frameworks. R software facilitated all numerical analyses and visualizations of data suited to environmental data modeling.

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8

Ashraf, Mohammed Shareef. "Estimation of Mixed (Burr type XII and Exponential) Distribution Parameters." European Journal of Theoretical and Applied Sciences 2, no. 6 (2024): 747–54. https://doi.org/10.59324/ejtas.2024.2(6).66.

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Many mixed distributions with various number of parameters can be generated from current distributions using the blending parameters 𝑠𝑠𝑤𝑤; where 0≤𝑠𝑠𝜋𝜋≤1 and Σ𝑠𝑠𝜋𝜋𝐾𝐾𝐾 𝑤𝑤=1=1. This research goals to utilize the concept of combining two distributions (Burr type XII and Exponential) with unbalanced scale coefficients to obtain a mixed distribution. These generated distributions were combined using the blending parameter 𝑤𝑤𝑘𝑘 which determines the percentage of contribution rate of each distribution to the resulting distribution. The significance of this study lies in developing a more adaptable distribution that can be used in statistical applications. Two estimation methods, namely maximum likelihood estimation (MLE) and ordinary least squares (OLS), were used to estimate the parameters of the generating mixed distribution. Simulation studies were also conducted to verify the properties of the generating mixed distribution and utilize the two estimating methods to estimate its parameters.

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9

Sánchez, Ewin. "Burr type-XII as a superstatistical stationary distribution." Physica A: Statistical Mechanics and its Applications 516 (February 2019): 443–46. http://dx.doi.org/10.1016/j.physa.2018.10.044.

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10

Al-Hussaini, Essam K. "A characterization of the Burr type XII distribution." Applied Mathematics Letters 4, no. 1 (1991): 59–61. http://dx.doi.org/10.1016/0893-9659(91)90123-d.

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11

Polosin, Vitaly G., Alexander N. Mitroshin, and Sergey I. Gerashchenko. "Burr Type XII Distribution in Traffic Control Systems." Transportation Research Procedia 68 (2023): 433–40. http://dx.doi.org/10.1016/j.trpro.2023.02.058.

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12

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.

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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.

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13

Kumar, Devendra. "The Burr Type Xii Distribution with Some Statistical Properties." Journal of Data Science 15, no. 3 (2021): 509–34. http://dx.doi.org/10.6339/jds.201707_15(3).0008.

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14

Para, Bilal Ahmad, Zahoor Ahmad, and Tariq Rashid Jan. "Discrete Burr Type XII Beta Distribution: Properties and Applications." Applied Mathematics & Information Sciences Letters 6, no. 3 (2018): 131–42. http://dx.doi.org/10.18576/amisl/060305.

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15

M.S., RAVIKUMAR, and KANTAM R.R.L. "Extreme Value Control Chart for Burr Type XII Distribution." i-manager’s Journal on Mathematics 5, no. 4 (2016): 47. http://dx.doi.org/10.26634/jmat.5.4.8309.

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16

Refaie, Mohamed K. A. "A New Extension of the Burr Type XII Distribution." Journal of Mathematics and Statistics 14, no. 1 (2018): 261–74. http://dx.doi.org/10.3844/jmssp.2018.261.274.

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17

Kumar, Surinder, Naresh Chandra, and M. J. S. Khan. "On the Reliability Estimation of Burr Type XII Distribution." Safety and Reliability 33, no. 2 (2013): 29–40. http://dx.doi.org/10.1080/09617353.2013.11716253.

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18

Pant, Mohan D., and Todd C. Headrick. "A Method for Simulating Burr Type III and Type XII Distributions through -Moments and -Correlations." ISRN Applied Mathematics 2013 (May 22, 2013): 1–14. http://dx.doi.org/10.1155/2013/191604.

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This paper derives the Burr Type III and Type XII family of distributions in the contexts of univariate -moments and the -correlations. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of -skew, -kurtosis, and -correlations. The procedure can be applied in a variety of settings such as statistical modeling (e.g., forestry, fracture roughness, life testing, operational risk, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that -moment-based Burr distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed procedure also demonstrates that the estimates of -skew, -kurtosis, and -correlation are substantially superior to their conventional product moment-based counterparts of skew, kurtosis, and Pearson correlations in terms of relative bias and relative efficiency—most notably when heavy-tailed distributions are of concern.

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19

Lio, Yuhlong, Tzong-Ru Tsai, Liang Wang, and Ignacio Pascual Cecilio Tejada. "Inferences of the Multicomponent Stress–Strength Reliability for Burr XII Distributions." Mathematics 10, no. 14 (2022): 2478. http://dx.doi.org/10.3390/math10142478.

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Multicomponent stress–strength reliability (MSR) is explored for the system with Burr XII distributed components under Type-II censoring. When the distributions of strength and stress variables have Burr XII distributions with common or unequal inner shape parameters, the existence and uniqueness of the maximum likelihood estimators are investigated and established. The associated approximate confidence intervals are obtained by using the asymptotic normal distribution theory along with the delta method and parametric bootstrap procedure, respectively. Moreover, alternative generalized pivotal quantities-based point and confidence interval estimators are developed. Additionally, a likelihood ratio test is presented to diagnose the equivalence of both inner shape parameters or not. Conclusively, Monte Carlo simulations and real data analysis are conducted for illustration.

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20

Jamal, Farrukh, Mohammed Reyad, Soha Othman Ahmed, and Syed Muhammad Akbar Ali Shah. "MATHEMATICAL PROPERTIES AND APPLICATIONS OF MINIMUM GUMBEL BURR DISTRIBUTION." NED University Journal of Research XVII, no. 2 (2020): 1–14. http://dx.doi.org/10.35453//nedjr-ascn-2018-0063.

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This paper presents the details of a proposed continuous model for the minimum Gumbel Burr distribution which is based on four different parameters. The model is obtained by compounding the Gumbel type-II and Burr-XII distributions. Basic mathematical properties of the new distribution were studied including the quantile function, ordinary and incomplete moments, moment generating function, order statistics, Rényi entropy, stress-strength model and stochastic ordering. The parameters of the proposed distribution are estimated using the maximum likelihood method. A Monte Carlo simulation was presented to examine the behaviour of the parameter estimates. The flexibility of the proposed model was assessed by means of three applications.

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21

Jamal, Farrukh, Hesham Mohammed Reyad, Soha Othman Ahmed, and Syed Muhammad Akbar Ali Shah. "MATHEMATICAL PROPERTIES AND APPLICATIONS OF MINIMUM GUMBEL BURR DISTRIBUTION." NED University Journal of Research XVII, no. 2 (2020): 1–14. http://dx.doi.org/10.35453/nedjr-ascn-2018-0063.

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This paper presents the details of a proposed continuous model for the minimum Gumbel Burr distribution which is based on four different parameters. The model is obtained by compounding the Gumbel type-II and Burr-XII distributions. Basic mathematical properties of the new distribution were studied including the quantile function, ordinary and incomplete moments, moment generating function, order statistics, Rényi entropy, stress-strength model and stochastic ordering. The parameters of the proposed distribution are estimated using the maximum likelihood method. A Monte Carlo simulation was presented to examine the behaviour of the parameter estimates. The flexibility of the proposed model was assessed by means of three applications.

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22

SRIVASTAVA, PREETI WANTI, and DEEPMALA SHARMA. "BILEVEL PROGRAMMING BASED TIME CENSORED STEP-STRESS PALTSP USING TAMPERED FAILURE RATE MODEL AND WARRANTY." International Journal of Reliability, Quality and Safety Engineering 21, no. 05 (2014): 1450022. http://dx.doi.org/10.1142/s0218539314500223.

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This paper deals with optimal design of time-censored step-stress partially accelerated life test sampling plan (PALTSP) using Burr type-XII life distribution. The Burr type XII distribution has been found appropriate for modeling failures that occur with less frequency and also when there is high occurrence of early failures. This distribution has been found appropriate for accelerated life testing experiments. The optimum sampling plan obtained using bilevel programming approach consists in finding optimum sample size and optimum stress change point by minimizing expected total cost per lot comprising warranty costs with respect to acceptance or rejection of the lot, sampling cost and testing cost such that the producer's and consumer's interested are safeguarded. The methods developed has been illustrated using an example and sensitivity analyses carried out.

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23

SRIVASTAVA, P. W., and N. MITTAL. "OPTIMUM MULTI-LEVEL RAMP-STRESS ALT PLAN WITH MULTIPLE-OBJECTIVES FOR BURR TYPE-XII DISTRIBUTION UNDER TYPE-I CENSORING." International Journal of Reliability, Quality and Safety Engineering 19, no. 02 (2012): 1250006. http://dx.doi.org/10.1142/s0218539312500064.

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This paper considers optimal design for ramp-stress accelerated life test (ALT) with multiple stresses and multiple estimating objectives using Burr type-XII life distribution and Type-I censoring. It is impractical to estimate only one objective parameter after conducting such costly ALT tests, therefore, an optimum ramp-stress ALT plan with multiple estimating objectives has been formulated. The need to analyze an ALT data with different life distribution models such as exponential, normal, Weibull, log logistic, etc., is necessitated since the use of correct life distribution model especially in the presence of a limited source of data-as typically occurs with modern devices, having high reliability, helps in preventing the choice of unnecessary and expensive planned replacements. The Burr type-XII distribution has a nonmonotone hazard function, which can accommodate many shapes of hazard function. The commonly used Weibull and exponential distributions are its limiting cases and log logistic distribution is its particular case. The distribution has been found appropriate for modeling failures that occur with less frequency and also when there is high occurrence of early failures. The inverse power law and a cumulative exposure model are assumed. The optimal test plan chooses the stress rates and proportion of units allocated to each stress by minimizing the weighted sum of the asymptotic variances of the maximum likelihood estimator of quantile lifetimes at design constant stress. The method developed has been illustrated using an example, sensitivity analysis carried out and comparative study has also been done to highlight the merits of the proposed model.

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24

Para, B. A., and T. R. Jan. "Discrete Burr Type XII Minimax Distribution: A New Discrete Model." Journal of Statistics Applications & Probability 6, no. 3 (2017): 635–46. http://dx.doi.org/10.18576/jsap/060318.

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25

Shareef, Ashraf Mohammed. "Estimation of Mixed (Burr type XII and Exponential) Distribution Parameters." European Journal of Theoretical and Applied Sciences 2, no. 6 (2024): 747–54. https://doi.org/10.59324/ejtas.2024.2(6).66.

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26

Danish, Muhammad Yameen, Irshad Ahmad Arshad, and Muhammad Aslam. "Bayesian inference for the randomly censored Burr-type XII distribution." Journal of Applied Statistics 45, no. 2 (2017): 270–83. http://dx.doi.org/10.1080/02664763.2016.1275530.

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27

Prakash, Gyan. "Bound lengths for Burr-XII distribution under step-stress PALT." International Journal of Scientific World 5, no. 2 (2017): 135. http://dx.doi.org/10.14419/ijsw.v5i2.8242.

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Some inferences based on Step-Stress Partially Accelerated Life Test (SS-PALT) are discussed in the present article. The Progressive Type-II censoring criterion with Random Removal scheme is used for determining the Approximate Confidence Lengths and One-Sample Bayes Prediction Bound Lengths for the unknown parameters of the Burr Type-XII distribution. Based on the simulated data, the analysis of the present discussion has been carried out.

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28

Kannan, K. Senthamarai, and A. Jabarali. "Evaluation of teletraffic queueing model under Burr type XII service distribution." Journal of Statistics and Management Systems 21, no. 1 (2018): 1–13. http://dx.doi.org/10.1080/09720510.2017.1386876.

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29

Zhao, Xiangyu, Masakazu Fujii, Yusuke Suganuma, Xiang Zhao, and Zhaoxia Jiang. "Applying the Burr Type XII Distribution to Decompose Remanent Magnetization Curves." Journal of Geophysical Research: Solid Earth 123, no. 10 (2018): 8298–311. http://dx.doi.org/10.1029/2018jb016082.

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30

Kayal, T., Yogesh Mani Tripathi, M. K. Rastogi, and A. Asgharzadeh. "Inference for Burr XII distribution under Type I progressive hybrid censoring." Communications in Statistics - Simulation and Computation 46, no. 9 (2017): 7447–65. http://dx.doi.org/10.1080/03610918.2016.1241405.

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31

Xin, Hua, Zhifang Liu, Yuhlong Lio, and Tzong-Ru Tsai. "Accelerated Life Test Method for the Doubly Truncated Burr Type XII Distribution." Mathematics 8, no. 2 (2020): 162. http://dx.doi.org/10.3390/math8020162.

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The Burr type XII (BurrXII) distribution is very flexible for modeling and has earned much attention in the past few decades. In this study, the maximum likelihood estimation method and two Bayesian estimation procedures are investigated based on constant-stress accelerated life test (ALT) samples, which are obtained from the doubly truncated three-parameter BurrXII distribution. Because computational difficulty occurs for maximum likelihood estimation method, two Bayesian procedures are suggested to estimate model parameters and lifetime quantiles under the normal use condition. A Markov Chain Monte Carlo approach using the Metropolis–Hastings algorithm via Gibbs sampling is built to obtain Bayes estimators of the model parameters and to construct credible intervals. The proposed Bayesian estimation procedures are simple for practical use, and the obtained Bayes estimates are reliable for evaluating the reliability of lifetime products based on ALT samples. Monte Carlo simulations were conducted to evaluate the performance of these two Bayesian estimation procedures. Simulation results show that the second Bayesian estimation procedure outperforms the first Bayesian estimation procedure in terms of bias and mean squared error when users do not have sufficient knowledge to set up hyperparameters in the prior distributions. Finally, a numerical example about oil-well pumps is used for illustration.

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32

Nagy, M., M. E. Bakr, and Adel Fahad Alrasheedi. "Analysis with Applications of the Generalized Type-II Progressive Hybrid Censoring Sample from Burr Type-XII Model." Mathematical Problems in Engineering 2022 (February 18, 2022): 1–21. http://dx.doi.org/10.1155/2022/1241303.

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In this article, based on the generalized Type-II progressive hybrid censoring sample from the Burr Type-XII distribution, maximum likelihood and Bayesian inference are discussed. Point and interval estimates of unknown parameters, reliability, and hazard functions are developed. We employed several loss functions, such as squared error, LINEX, and general entropy, as symmetric and asymmetric loss functions and various prior distributions as informative and non-informative priors for Bayesian inference of unknown parameters. Under a generalized Type-II progressive hybrid censoring sample, we also propose a Bayesian one-sample prediction for unobserved failures. We conduct simulation study using the MCMC algorithm for the Bayesian approach based on several prior distributions. Finally, we apply the results of the theoretical research to real data.

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33

Jang, Dong-Ho, Myoungjin Jung, Ji-Hoon Park, and Chansoo Kim. "Bayesian estimation of Burr type XII distribution based on general progressive type II censoring." Applied Mathematical Sciences 8 (2014): 3435–48. http://dx.doi.org/10.12988/ams.2014.44261.

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34

An, Jeong-Hyang. "Two model comparisons of software reliability analysis for Burr type XII distribution." Journal of the Korean Data and Information Science Society 23, no. 4 (2012): 815–23. http://dx.doi.org/10.7465/jkdi.2012.23.4.815.

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35

Soliman, Ahmed A., Ahmed H. Abd Ellah, Naser A. Abou-Elheggag, and Abdullah A. Modhesh. "Estimation from Burr type XII distribution using progressive first-failure censored data." Journal of Statistical Computation and Simulation 83, no. 12 (2013): 2270–90. http://dx.doi.org/10.1080/00949655.2012.690157.

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36

Panahi, Hanieh, and Abdolreza Sayyareh. "Estimation and prediction for a unified hybrid-censored Burr Type XII distribution." Journal of Statistical Computation and Simulation 86, no. 1 (2015): 55–73. http://dx.doi.org/10.1080/00949655.2014.993985.

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37

Prakash, Gyan. "Progressive Censored Burr Type-XII Distribution Under Random Removal Scheme: Some Inferences." Afrika Statistika 12, no. 2 (2017): 1273–84. http://dx.doi.org/10.16929/as/2017.1273.104.

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38

Rastogi, Manoj Kumar, and Yogesh Mani Tripathi. "Estimating a parameter of Burr type XII distribution using hybrid censored observations." International Journal of Quality & Reliability Management 28, no. 8 (2011): 885–93. http://dx.doi.org/10.1108/02656711111162532.

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39

Balakrishnan, Narayanaswamy, Nan Jiang, Tzong-Ru Tsai, Y. L. Lio, and Ding-Geng Chen. "Reliability Inference on Composite Dynamic Systems Based on Burr Type-XII Distribution." IEEE Transactions on Reliability 64, no. 1 (2015): 144–53. http://dx.doi.org/10.1109/tr.2014.2338251.

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40

Wingo, Dallas R. "Maximum likelihood estimation of Burr XII distribution parameters under Type II censoring." Microelectronics Reliability 33, no. 9 (1993): 1251–57. http://dx.doi.org/10.1016/0026-2714(93)90126-j.

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41

Abdel-Ghaly, A. A., G. R. Al-Dayian, and F. H. Al-Kashkari. "The use of Burr type XII distribution on software reliability growth modelling." Microelectronics Reliability 37, no. 2 (1997): 305–13. http://dx.doi.org/10.1016/0026-2714(95)00124-7.

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42

Noori Asl, M., R. Arabi Belaghi, and H. Bevrani. "On Burr XII Distribution Analysis Under Progressive Type-II Hybrid Censored Data." Methodology and Computing in Applied Probability 19, no. 2 (2016): 665–83. http://dx.doi.org/10.1007/s11009-016-9514-7.

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43

Xin, Hua, Jianping Zhu, Junge Sun, Chenlu Zheng, and Tzong-Ru Tsai. "Reliability Inference Based on the Three-Parameter Burr Type XII Distribution with Type II Censoring." International Journal of Reliability, Quality and Safety Engineering 25, no. 02 (2018): 1850010. http://dx.doi.org/10.1142/s0218539318500109.

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The three-parameter Burr type XII distribution (3pBXIID) is quite flexible and contains a wide range of distribution shapes for fitting lifetime data. However, it is difficult to obtain reliable estimates of the 3pBXIID quantiles from censored samples for evaluating the reliability of lifetime data. In this work, a Metropolis–Hastings Markov chain Monte Carlo (M-H MCMC) procedure is proposed to obtain reliable maximum likelihood estimates (MLEs) of the 3pBXIID quantiles from a type II censored sample. Moreover, the parametric bootstrap percentile procedure is used to obtain the confidence interval of the quantile of the 3pBXIID. The performance of the proposed M-H MCMC method is evaluated in view of Monte Carlo simulations. Two examples, regarding the survival lifetimes of breast cancer patients and the reliability inference on the lifetimes of oil-well pumps for sucker-rod oil pumping systems, are applied to illustrate the applications of the proposed M-H MCMC method and bootstrap procedure.

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44

Wang, Xinjing, and Wenhao Gui. "Bayesian Estimation of Entropy for Burr Type XII Distribution under Progressive Type-II Censored Data." Mathematics 9, no. 4 (2021): 313. http://dx.doi.org/10.3390/math9040313.

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With the rapid development of statistics, information entropy is proposed as an important indicator used to quantify information uncertainty. In this paper, maximum likelihood and Bayesian methods are used to obtain the estimators of the entropy for a two-parameter Burr type XII distribution under progressive type-II censored data. In the part of maximum likelihood estimation, the asymptotic confidence intervals of entropy are calculated. In Bayesian estimation, we consider non-informative and informative priors respectively, and asymmetric and symmetric loss functions are both adopted. Meanwhile, the posterior risk is also calculated to evaluate the performances of the entropy estimators against different loss functions. In a numerical simulation, the Lindley approximation and the Markov chain Monte Carlo method were used to obtain the Bayesian estimates. In turn, the highest posterior density credible intervals of the entropy were derived. Finally, average absolute bias and mean square error were used to evaluate the estimators under different methods, and a real dataset was selected to illustrate the feasibility of the above estimation model.

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Zoramawa, A.B, and A. S. Charanchi. "A Study on Sequential Probability Sampling for Monitoring a Resubmitted Lots under Burr-Type XII Distribution." Continental J. Applied Sciences 16, no. 2 (2021): 16–26. https://doi.org/10.5281/zenodo.5540382.

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<em>In this research, Sequential probability sampling analysis was used to treat the sample size obtained from either single or double sampling plans. Precisely the research considers and compared the minimum sample obtained from Bur Type XII distribution. Estimations of minimum sample, acceptance and rejection numbers obtained were analyzed and presented to explain the usefulness of sequential plans in relation to single and double sampling plan. Average Sample Number (ASN) obtained indicated the hypothesis at various risks’ levels was accepted indicating there is a time limit to terminate the sampling. Sequential probability sampling (SPS) plays a vital role at any sampling plan obtained using Bur Type XII distribution and saves inspection time</em><em> which was among the major concern of both producers and consumers in the manufacturing industries.</em>

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Abdel-Hamid, Alaa H. "Constant-partially accelerated life tests for Burr type-XII distribution with progressive type-II censoring." Computational Statistics & Data Analysis 53, no. 7 (2009): 2511–23. http://dx.doi.org/10.1016/j.csda.2009.01.018.

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Abdallah Abdelfattah and Nagwan Reyad Elshendidy. "An Estimation of Parameters For Exponentiated Burr Type XII Distribution Based on Ranked Set Sampling." JOURNAL OF ADVANCES IN MATHEMATICS 19 (August 15, 2020): 26–34. http://dx.doi.org/10.24297/jam.v19i.8828.

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The aim of this paper is to estimate the parameters of exponentiated Burr type XII distribution (EBXII) based on ranked set sampling (RSS) technique, and also simple random sampling(SRS) is provided by the method of maximum likelihood. Fisher information matrix for both (SRS) and (RSS) for the unknown parameters are derived. Simulation study compared between the estimators of both methods in terms of their biases, mean square errors, and efficiencies. It is shown that the estimators based on RSS are more efficient than those of SRS.

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Nassir, Layla M., Husam Abdulrazzak Rasheed, and Aseel Abdul Razzak Rasheed. "The effect of polluted samples on Bayesian Estimators of Burr type –XII distribution." Periodicals of Engineering and Natural Sciences (PEN) 10, no. 2 (2022): 337. http://dx.doi.org/10.21533/pen.v10i2.2862.

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Hussain, Wafaa J., Ahmed A. Akkar, and Husam A. Rasheed. "Comparison of Robust and Bayesian Methods for Estimating the Burr Type XII Distribution." International Journal on Advanced Science, Engineering and Information Technology 10, no. 5 (2020): 1835. http://dx.doi.org/10.18517/ijaseit.10.5.12990.

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Akgül, Fatma Gül, Şükrü Acıtaş, and Birdal Şenoğlu. "Estimation of the location and the scale parameters of Burr Type XII distribution." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 68, no. 1 (2018): 1030–44. http://dx.doi.org/10.31801/cfsuasmas.501455.

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