Bayesian prediction intervals of order statistics based on progressively type-II censored competing risks data from the half-logistic distribution

Abstract The competing risks model may be of great importance for an investigator in medical studies or in reliability analysis. In this article, Bayesian prediction bounds of order statistics based on progressively type-II censored competing risks data from a general class of distributions are obtained. The class of distributions includes, among others, Weibull, compound Weibull, Pareto, Gompertz, compound Gompertz and half-logistic distributions. The results are then applied to the half-logistic distribution. Based on three different progressive type-II censoring schemes, prediction intervals of the future order statistics are obtained. An illustrative example is presented to show the procedure. A Monte Carlo simulation study is performed and numerical computations are carried out to obtain the coverage probabilities and average interval lengths of the prediction intervals.

[1]  E. K. Al-Hussaini,et al.  Predicting observables from a general class of distributions , 1999 .

[2]  J. Bert Keats,et al.  Statistical Methods for Reliability Data , 1999 .

[3]  N. Balakrishnan,et al.  Progressive Censoring: Theory, Methods, and Applications , 2000 .

[4]  Dennis V. Lindley,et al.  Empirical Bayes Methods , 1974 .

[5]  Mohammad Z. Raqab,et al.  Prediction for Pareto distribution based on progressively Type-II censored samples , 2010, Comput. Stat. Data Anal..

[6]  N. Balakrishnan,et al.  Predictors of Failure Times of Censored Units in Progressively Censored Samples from Normal Distribution , 2010 .

[7]  Narayanaswamy Balakrishnan,et al.  A Simple Simulational Algorithm for Generating Progressive Type-II Censored Samples , 1995 .

[8]  Alaa H. Abdel-Hamid,et al.  Progressive stress accelerated life tests under finite mixture models , 2007 .

[9]  E. Kay,et al.  Methods for statistical analysis of reliability and life data , 1974 .

[10]  Debasis Kundu,et al.  Bayesian Inference and Life Testing Plan for the Weibull Distribution in Presence of Progressive Censoring , 2008, Technometrics.

[11]  Z. F. Jaheen.  Prediction of Progressive Censored Data from the Gompertz Model , 2003 .

[12]  N. Singpurwalla,et al.  Methods for Statistical Analysis of Reliability and Life Data. , 1975 .

[13]  Alaa H. Abdel-Hamid,et al.  Bayesian prediction for type-II progressive-censored data from the Rayleigh distribution under progressive-stress model , 2014 .

[14]  J. Lawless.  Statistical Models and Methods for Lifetime Data , 2002 .

[15]  Thomas A. Louis,et al.  Empirical Bayes Methods , 2006 .

[16]  Erhard Cramer,et al.  Progressively Type-II censored competing risks data from Lomax distributions , 2011, Comput. Stat. Data Anal..

[17]  J. Boag,et al.  Maximum Likelihood Estimates of the Proportion of Patients Cured by Cancer Therapy , 1949 .

[18]  D G Hoel,et al.  A representation of mortality data by competing risks. , 1972, Biometrics.

[19]  N. Balakrishnan,et al.  On some predictors of times to failure of censored items in progressively censored samples , 2006, Comput. Stat. Data Anal..

[20]  Essam K. Al-hussinp,et al.  On the median of a finite mixture , 1997 .

[21]  W. Nelson.  Statistical Methods for Reliability Data , 1998 .

[22]  Narayanaswamy Balakrishnan,et al.  Analysis of Progressively Censored Competing Risks Data , 2003, Advances in Survival Analysis.

[23]  M. A. M. Ali Mousa,et al.  Inference and prediction for pareto progressively censored data , 2001 .

[24]  Sumit Kumar,et al.  Author's Personal Copy Computational Statistics and Data Analysis on Progressively Censored Competing Risks Data for Weibull Distributions , 2022 .