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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
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
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
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