Robust Bayesian Analysis of Generalized Half Logistic Distribution

  • Ajit Chaturvedi University of Delhi
  • Taruna Kumari University of Delhi
DOI: https://doi.org/10.19139/soic.v5i2.268
Keywords: GHLD, Ɛ-contamination class of priors, ML-II posterior density, Hazard-rate, Reliability function, SELF and LINEX losses, type-II censoring, sampling scheme by Bartholomew, Markov Chain Monte Carlo (MCMC) procedure, Metropolis-Hastings algorithm.

Abstract

In this paper, Robust Bayesian analysis of the generalized half logistic distribution (GHLD) under an $\epsilon$-contamination class of priors for the shape parameter $\lambda$ is considered. ML-II Bayes estimators of the parameters, reliability function and hazard function are derived under the squared-error loss function (SELF) and linear exponential (LINEX) loss function by considering the Type~II censoring and the sampling scheme of Bartholomew (1963). Both the cases when scale parameter is known and unknown is considered under Type~II censoring and under the sampling scheme of Bartholomew. Simulation study and analysis of a real data set are presented.

Author Biographies

Ajit Chaturvedi, University of Delhi
Statistics, Assosiate Professor
Taruna Kumari, University of Delhi
Statistics, Assistant Professor

References

S.H. Arora, G.C. Bhimani, and M.N. Patel, Some results on maximum likelihood estimators of parameters of generalized half logistic distribution under Type-I progressive censoring with changing, International Journal of Contemporary Mathematical Sciences, vol.

, pp. 685–698, 2010.

A. Asgharzadeh, R. Rezaie, and M. Abdi, Comparisons of methods of estimation for the half-logistic distribution, Selc¸uk J. Appl. Math., Special Issue, pp. 93–108, 2011.

R. Azimi, Bayesian estimation of generalized half logistic type-II doubly censored data, International Journal of Scientific World,vol. 1, pp. 57–60, 2013.

N. Balakrishnan, Order statistics from the half logistic distribution, Journal of Statistics and Computer Simulation, vol. 20, pp.287–309, 1985.

N. Balakrishnan, and A. Asgharzadeh, Inference for the scaled half-logistic distribution based on progressively type II censored samples, Comunication in Statistics-Theory and Methods, vol. 34, pp. 73–87, 2005.

N. Balakrsihnan, and A. Hossain, Inference for the Type-II generalized logistic distribution under progressive Type-II censoring, Journal of Statistical Computation and Simulation, vol. 77, pp. 1013–1031, 2007.

N. Balakrishnan, and N. Kannan, Point and interval estimation for the logistic distribution based on progressively Type-II censored samples, in Handbook of Statistics, N. Balakrishnan and C. R. Rao, Eds., vol. 20, pp. 431–456, 2001.

N. Balakrishnan, N. Kannan, C.T. Lin, and S.J.S. Wu, Inference for the extreme value distribution under progressively Type-II censoring, Journal of Statistical Computation and Simulation, vol. 74, pp. 25–45, 2004.

N. Balakrishnan, and N. Puthenpura, Best linear unbiased estimators of location and scale parameters of the half logistic distribution, Journal of Statistics and Computer Simulation, vol. 25, pp. 193–204, 1986.

D.J. Bartholomew, The sampling distribution of an estimate arising in life testing, Technometrics, vol. 5, pp. 361–374, 1963.

J.O. Berger, Bayesian robustness and Stein effect, J. Am. Stat. Assoc., vol. 77, pp. 358–368, 1982.

J.O. Berger, The robust Bayesian viewpoint (with discussion), In: Kadane, J. (ed.) Robustness in Bayesian Statistics, North Holland,1983.

J.O. Berger, Statistical Decision Theory and Bayesian Analysis, New York: Springer-Verlag, 1985.

J.O. Berger, and J.M. Berliner, Robust Bayes and empirical Bayes analysis with ϵ-contaminated priors, Technical Report No. 83–85, Department of Statistics, Purdue University, West Lafayette, 1983.

J.O. Berger, D.R. Insua, and F. Ruggeri, Bayesian robustness. In: Rios Insua, D., Ruggeri, F. (eds.), Robust Bayesian Analysis,Lecture Notes in Statistics, vol. 152, pp. 1–32. Springer, New York, 2000.

B. Betro, Numerical treatment of Bayesian robustness problems, Int. J. Approx. Reason., vol. 50, pp. 279–288, 2009.

G.E.P. Box, and G.C. Tiao, A further look at robustness in Bayes theorem, Biometrica, vol. 49, pp. 419–432, 1962.

G.E.P. Box, Sampling and Bayes inferences in scientific modeling and robustness (with discussion), J. Roy. Stat. Soc., vol. B41, pp.113–147, 1980.

A. Chaturvedi, Robust Bayesian analysis of the linear regression model, J. Stat. Plan. Infer., vol. 50, pp. 175–186, 1993.

A. Chaturvedi, Robust Bayesian analysis of the Exponential failure model, Pak. J. Stat. vol. 14, no. 24, pp. 115–126, 1998.

A. Chaturvedi, S.B. Kang, and A. Pathak, Estimation and testing procedures for the reliability functions of generalized half logistic distribution, Journal of The Korean Statistical Society, vol. 45, pp. 314–328, 2016.

A. Chaturvedi, M. Pati, and S.K. Tomer, Robust Bayesian analysis of Weibull failure model, METRON. DOI 10.1007/s40300-013-0027-7, 2013.

A.P. Dempster, Examples relevant to the robustness of applied inferences, In: Gupta, S.S., Berger, J.O. (eds.) Stat. Decis. TheoryRelat. Topics III. Academic Press, NY, 1976.

I.J. Good, Probability and the Weighting of Evidence, Griffin: London, 1950.

I.J. Good, The estimation of Probability, MIT Press, Cambridge, 1965.

I.J. Good, A Bayesian significance test for multinomial distributions, J. Roy. Stat. Soc., vol. B-29, pp. 399–443, 1967.

I.J. Good, Some history of the hierarchical Bayesian methodology, In: J.M. Bernardo, M.H. DeGroot, D.V. Lindley, A.F.M. Smith(eds.), Bayesian Statistics. University Press, Valencia, 1980.

H. Jeffreys, Theory of Probability, 3rd edn., Clarendon Press, Oxford, 1961.

Y. Kim, S.B. Kang, and J.I. Seo, Bayesian estimation in the generalized half logistic distribution under progressively Type II censoring, Journal of the Korean Data and Information Science Society, vol. 22, pp. 977–987, 2011.

D.V. Lindley, The robustness of interval estimates, Bull. Int. Stat. Inst., vol. 38, pp. 209–220, 1961.

W.B. Nelson, Applied Life Data Analysis, John Willey and Sons, New York, 1982.

J.I. Seo, and S.B. Kang, Entropy estimation of generalized half-logistic distribution (GHLD) bassed on Type-II censored samples, Entropy, vol. 16, pp. 443–454, 2014.

J.I. Seo, Y. Kim, and S.B. Kang, Estimation on the generalized half logistic distribution under Type-II hybrid censoring, Communications for Statistical Applications and Methods, vol. 20, pp. 63–75, 2013.

J.I. Seo, H.J. Lee, and S.B. Kang, Estimation for generalized half logistic distribution based on records, Journal of the Korean Data and Information Science Society, vol. 23, pp. 1249–1257, 2012.

Published
2017-06-01
How to Cite
Chaturvedi, A., & Kumari, T. (2017). Robust Bayesian Analysis of Generalized Half Logistic Distribution. Statistics, Optimization & Information Computing, 5(2), 158-178. https://doi.org/10.19139/soic.v5i2.268
Issue
Vol 5 No 2 (2017)
Section
Research Articles
Authors who publish with this journal agree to the following terms:

    1. 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.
    2. 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.
    3. 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).