Statistical Inference of Chen Distribution Based on Type I Progressive Hybrid Censored Samples
Abstract
In this paper we study the problem of estimating unknown parameters of a two-parameter distribution with bathtub shape under the assumption that data are type I progressive hybrid censored. We derive maximum likelihood estimators and then obtain the observed Fisher information matrix. Bayes estimators are also obtained under the squared error loss function and highest posterior density intervals are constructed as well. We perform a simulation study to compare proposed methods and analyzed a real data set for illustration purposes. Finally we establish optimal plans with respect to cost constraints and obtain comments based on a numerical study.References
A. M. Almarashi, A. Algarni, H. Okasha, M. Nassar, On reliability estimation of Nadarajah–Haghighi distribution under adaptive type-I progressive hybrid censoring scheme, Qual. Reliab. Eng. Int., DOI: 10.1002/qre.3016, 2022.
C. Lodhi ,Y. M. Tripathi, L. Wang, Inference for a general family of inverted exponentiated distributions with partially observed competing risks under generalized progressive hybrid censoring, J. Statist. Comput. Simul., vol. 91, 2503-2526, 2021.
J. G´orny and E. Cramer, Modularization of hybrid censoring schemes and its application to unified progressive hybrid censoring, Metrika, vol. 81, 173-210, 2018.
S. Basu, S. K. Singh, U. Singh, Bayesian inference using product of spacings function for Progressive hybrid Type-I censoring scheme, Statistics, vol. 52, 345-363, 2017.
A. Koley and D.Kundu, On generalized progressive hybrid censoring in presence of competing risks, Metrika, vol. 80, 401-426, 2017.
E. A. Ahmed, Bayesian estimation based on progressive type II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach, J. Appl. Stat., vol. 41, 752-768, 2014.
N. Balakrishnan and R. Aggarwala, Progressive Censoring: Theory, Methods, and Applications, Boston: Birkh¨auser, 2000.
N. Balakrishnan, Progressive censoring methodology: an appraisal, Test, vol. 16, 211-259, 2007.
M.H. Chen, Q. M. Shao, Monte Carlo estimation of Bayesian credible and HPD intervals, J. Comput. Graph. Statist., vol. 8, 69-92, 1999.
M. Bebbington, C.D. Lai, R. Zitikis, Useful periods for lifetime distributions with bathtub shaped hazard rate functions, IEEE Trans. Reliab., vol. 55(2), 245-251, 2006.
M. Bebbington, C.D. Lai, R. Zitikis, Modeling human mortality using mixtures of bathtub shaped failure distributions, J. Theor. Biol., vol. 245, pp. 528-538, 2007.
H. W. Block and T. H. Savits, Burn-in, Statist. Sci., vol. 12, pp. 1-19, 1997.
Z. Chen, A new two parameter lifetime distribution with bathtub shaped or increasing failure rate function, Statist. Probab. Lett., vol. 49, pp. 155-161, 2000.
D. J. Davis, An analysis of some failure data. J. Amer. Statist. Assoc., vol. 47, pp. 113-150, 1952.
A. P. Dempster, N. M. Laird and D. B. Rubin, Maximum likelihood from incomplete data via the EM algorithm J. Roy. Statist. Soc. Ser. B, vol. 39, pp. 1-38, 1977.
B. Epstein, Truncated life tests in the exponential case, Ann. Math. Stat., vol. 25, pp. 555-564, 1954.
D. J. Hand, F. Daly, A. D. Lunn, K. J. McConway and E. Ostrowski, A Handbook of Small Data Sets, London: Chapman & Hall, 255, 1994.
W. K. Hastings, Monte Carlo Sampling Methods Using Markov Chains and Their Applications, Biometrika, vol. 57, pp. 97-109, 1970.
U. Hjorth, A reliability distribution with increasing, decreasing, constant and bathtub-shaped failure rates, Technometrics, vol. 22, pp. 99-107, 1980.
T. Kayal, Y. M. Tripathi, M. K. Rastogi and A. Asgharzadeh, Inference for Burr XII distribution under type I progressive hybrid censoring, Commun. Stat. Simul. Comput., vol. 46(9), pp. 7447-7465, 2017.
T. Kayal, Y. M. Tripathi, D. P. Singh and M. K. Rastogi, Estimation and prediction for Chen distribution with bathtub shape under progressive censoring, J. Statist. Comput. Simul., vol. 87(2), pp. 348-366, 2017.
D. Kundu and A. Joarder, Analysis of Type-II progressively hybrid censored data, Comput. Stat. Data Anal., vol. 50, pp. 2509-2528, 2006.
D. Kundu, Bayesian inference and life testing plan for the Weibull distribution in presence of progressive censoring, Technometrics, vol. 50, pp. 144-154, 2008.
D. Kundu and B. Pradhan, Bayesian inference and life testing plans for generalized exponential distribution, Sci. China Ser. A: Mathematics, vol. 52, pp. 1373-1388, 2009.
C. T. Lin, C. C. Chou and Y. L. Huang, Inference for the Weibull distribution with progressive hybrid censoring, Comput. Stat. Data Anal., vol. 56, pp. 451-467, 2012.
T. A. Louis, Finding the observed matrix using the EM algorithm, J. Roy. Statist. Soc. Ser. B, vol. 44, pp. 226-233, 1982.
N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, Equations of state calculations by fast computing machines, J. Chem. Phy., vol. 21, pp. 1087-1092, 1953.
H. K. T. Ng, P. S. Chan and N. Balakrishnan, Estimation of parameters from progressively censored data using EM algorithm, Comput. Stat. Data Anal., vol. 39, pp. 371-386, 2002.
B. Pradhan and D. Kundu, On progressively censored generalized exponential distribution, Test, vol. 18, pp. 497-515, 2009.
S. Rajarshi and M. B. Rajarshi, Bathtub distributions: a review, Commun. Statist. Theory Methods, vol. 17, pp. 2597-2621, 1988.
M. K. Rastogi, Y. M. Tripathi and S. J. Wu, Estimating the parameters of a bathtub-shaped distribution under progressive type-II censoring, J. Appl. Stat. vol. 39, pp. 2389-2411, 2012.
R. M. Smith, and L. J. Bain, An exponential power life testing distribution, Commun. Statist. Theory Methods, vol. 4, pp. 469-481, 1975.
S. Singh, Y. M. Tripathi and S. J. Wu, On estimating parameters of a progressively censored lognormal distribution, J. Statist. Comput. Simul., vol. 85, pp. 1071-1089, 2015.
L. Tierney and J. Kadane, Accurate approximations for posterior moments and marginals, J. Amer. Statist. Assoc. vol. 81, pp. 82-86, 1986.
S. K. Tomer and M. S.Panwar, Estimation procedures for Maxwell distribution under type-I progressive hybrid censoring scheme, J. Statist. Comput. Simul., vol. 85(2), pp. 339-356, 2015.
S. J. Wu, Estimation of the two parameter bathtub-shaped lifetime distribution with progressive censoring, J. Appl. Stat., vol. 35, pp. 1139-1150, 2008.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
