Volume 6, Issue 3, May 2017, Page: 141-149
Estimation of the Parameters of Poisson-Exponential Distribution Based on Progressively Type II Censoring Using the Expectation Maximization (Em) Algorithm
Joseph Nderitu Gitahi, Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya
John Kung’u, Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya
Leo Odongo, Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya
Received: Mar. 16, 2017;       Accepted: Apr. 6, 2017;       Published: Apr. 27, 2017
DOI: 10.11648/j.ajtas.20170603.12      View  1748      Downloads  127
Abstract
This paper considers the parameter estimation problem of test units from Poisson-Exponential distribution based on progressively type II right censoring scheme. The maximum likelihood estimators (MLEs) for Poisson-Exponential parameters are derived using Expectation Maximization (EM) algorithm. EM-algorithm is also used to obtain the estimates as well as the asymptotic variance-covariance matrix. By using the obtained variance-covariance matrix of the MLEs, the asymptotic 95% confidence interval for the parameters are constructed. Through simulation, the behavior of these estimates are studied and compared under different censoring schemes and parameter values. It is concluded that for an increasing sample size; the estimated value of the parameters converges to the true value, the variances decrease and the width of the confidence interval become narrower.
Keywords
Poisson-Exponential Distribution, Progressive Type II Censoring, Maximum Likelihood Estimation, EM Algorithm
To cite this article
Joseph Nderitu Gitahi, John Kung’u, Leo Odongo, Estimation of the Parameters of Poisson-Exponential Distribution Based on Progressively Type II Censoring Using the Expectation Maximization (Em) Algorithm, American Journal of Theoretical and Applied Statistics. Vol. 6, No. 3, 2017, pp. 141-149. doi: 10.11648/j.ajtas.20170603.12
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
Kus, C. (2007). A new lifetime distribution. Computational Statistics and Data Analysis 51, 4497-4509.
[2]
Barreto, S. W. and Cribari, N. F. (2009). A generalization of Exponential-Poisson distribution. Statistics and Probability Letters 79, 2493-2500.
[3]
Cancho, V. G. Louzada-Neto, F. and Barriga, G. D. C. (2011). The Poisson-Exponential lifetime distribution. Computational Statistics and Data Analysis 55, 677-686.
[4]
Basu,A.,Klein, L. (1982). Some Recent Development in Competing Risks Theory. Survival Analysis,IMS, Hayward.
[5]
Adamidis,K.,Loukas, S. (1998). A Lifetime distribution with decreasing failure rate. Statistics and Probability Letters 39(1), 35-42.
[6]
Bain, L. T and Engelhardt, M. (1991). Statistical Analysis of Reliability and Life Testing Model, Marcel Dekker; New York.
[7]
Cohen. A. C. (1976). Progressively censored sampling in the three parameter lognormal distribution, Technometrics 18, 99-103.
[8]
Aggarwala, R. (2001). Progressively interval censoring: Some mathematical results with application to inference. Communications in Statistics-Theory and Methods 30, 1921-1935.
[9]
Amal, H. Samawi, H. and Mohammad, Z. R. (2013). Estimation on Lomax Progressive Censoring using E. M algorithm. The Journal of Statistical Computation and Simulation 1-18.
[10]
Balakrishnan N. (2007). Progressive censoring methodology: an appraisal (with discussion). TEST;16:211–259.
[11]
Louzada-Neto, F., Cancho, V. G. and Barrigac, G. D. C. (2011). The Poisson- Exponential distribution: a Bayesian approach. Journal of Applied Statistics 38, 1239-1248.
[12]
Singh S. K., Singh, U. and Manoj, K. M. (2014). Estimation for the Parameter of Poisson-Exponential Distribution under Bayesian Paradigm, Journal of Data Science 12, 157-173.
[13]
Raqab, M. Z. and Madi, T. M. (2011). Inference for the generalized Rayleigh distribution based on progressively censored data. Journal of Statistical Planning and Inference 141, 3313-3322.
[14]
Krishna. H and Kumar (2011). Reliability estimation in Lindley distribution with progressively type II right censored sample. Mathematics and Computers in Simulation 82(2), 281-294.
[15]
Kumar. K, Garg. R and Krishna, H. (2014). Estimation of parameters of Nakagami distribution with progressively censored samples. National conference on Statistical Inference, Sampling Techniques and Related Areas February, 18-19 at AMU Aligarh.
[16]
Pak, A., Gholam. A. P. and Mansour. S (2014). Inference for the Rayleigh Distribution Based on Progressive Type-II Fuzzy Censored Data. Journal of Modern Applied Statistical Methods 13(1), Article 19.
[17]
Rastogi, M. K. and Tripathi, Y. M. (2012). Estimating the parameters of Burr distribution under progressive type II censoring. Statistical Methodology 9,381-391.
[18]
Watanable M. and Yamaguchi K. (2004). The EM algorithm and related statistical models. New York: Marcel Dekker.
[19]
Ng K., Chan P. S and Balakrishnan N. (2002). Estimation of Parameters from progressively censored data using an EM algorithm. Computational Statistics and Data Analysis, 39 (4), 371-386.
[20]
Rubin D. B. (1991). EM and beyond. Psychometrika 56,241–254.
[21]
Rubin D. B. (1987). The SIR algorithm. Journal of American Statistical Association 82,543–546.
[22]
Tanner M. A and Wange W. H. (1987). The calculation of posterior distributions by data augmentation. Journal of American Statistical Association 82,528–550.
[23]
Balakrishnan, N. and Aggarwala, R. (2000). Progressive censoring: theory, methods, and applications. Birkhäuser, Boston.
[24]
Dempster, A. P, Laird, N. M and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, 39(1), 1–38.
[25]
McLachlan, G. J. and Krishnan, T. (1997). The EM Algorithm and Extension. Wiley, New York.
[26]
Sadegh, R. and Rasool, T. (2012). A New Lifetime Distribution with Increasing Failure Rate: Exponential Truncated Poisson. Journal of Basic and Applied Scientific Research 2(2), 1749-1762.
[27]
Cox, D. and Hinkley, D. (1979). Theoretical statistics, Chapman & Hall, London.
[28]
Louis, T. A. (1982). Finding the observed information matrix when using the EM algorithm. Journal of Royal Statistical Society 44, 226-233.
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