Parameter Estimation of Kumaraswamy Distribution Based on Progressive Type II Censoring Scheme Using Expectation-Maximization Algorithm
American Journal of Theoretical and Applied Statistics
Volume 5, Issue 3, May 2016, Pages: 154-161
Received: May 3, 2016; Accepted: May 23, 2016; Published: Jun. 1, 2016
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Authors
Wafula Mike Erick, Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya
Kemei Anderson Kimutai, Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya
Edward Gachangi Njenga, Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya
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Abstract
This project considers the parameter estimation problem of test units from Kumaraswamy distribution based on progressive Type-II censoring scheme. The progressive Type-II censoring scheme allows removal of units at intermediate stages of the test other than the terminal point. The Maximum Likelihood Estimates (MLEs) of the parameters are derived using Expectation-Maximization (EM) algorithm. Also the expected Fisher information matrix based on the missing value principle is computed. By using the obtained expected Fisher information matrix of the MLEs, asymptotic 95% confidence intervals for the parameters are constructed. Through simulations, the behaviour of these estimates are studied and compared under different censoring schemes and parameter values. It’s concluded that for an increasing sample; the estimated parameter values become closer to the true values, the variances and widths of the confidence intervals reduce. Also, more efficient estimates are obtained with censoring schemes concerned with removals of units from their right.
Keywords
Kumaraswamy Distribution, Progressive Type II Censoring, Maximum Likelihood Estimation, EM Algorithm
To cite this article
Wafula Mike Erick, Kemei Anderson Kimutai, Edward Gachangi Njenga, Parameter Estimation of Kumaraswamy Distribution Based on Progressive Type II Censoring Scheme Using Expectation-Maximization Algorithm, American Journal of Theoretical and Applied Statistics. Vol. 5, No. 3, 2016, pp. 154-161. doi: 10.11648/j.ajtas.20160503.21
Copyright
Copyright © 2016 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.
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