Parameter Estimation of Kumaraswamy Distribution Based on Progressive Type II Censoring Scheme Using Expectation-Maximization Algorithm

Wafula Mike Erick; Kemei Anderson Kimutai; Edward Gachangi Njenga

doi:doi:10.11648/j.ajtas.20160503.21

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Parameter Estimation of Kumaraswamy Distribution Based on Progressive Type II Censoring Scheme Using Expectation-Maximization Algorithm

Wafula Mike Erick, Kemei Anderson Kimutai, Edward Gachangi Njenga

Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 3)

Received: 3 May 2016 Accepted: 23 May 2016 Published: 1 June 2016

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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.

Published in	American Journal of Theoretical and Applied Statistics (Volume 5, Issue 3)
DOI	10.11648/j.ajtas.20160503.21
Page(s)	154-161
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Kumaraswamy Distribution, Progressive Type II Censoring, Maximum Likelihood Estimation, EM Algorithm

References

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APA Style

Wafula Mike Erick, Kemei Anderson Kimutai, Edward Gachangi Njenga. (2016). Parameter Estimation of Kumaraswamy Distribution Based on Progressive Type II Censoring Scheme Using Expectation-Maximization Algorithm. American Journal of Theoretical and Applied Statistics, 5(3), 154-161. https://doi.org/10.11648/j.ajtas.20160503.21

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ACS Style

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. Am. J. Theor. Appl. Stat. 2016, 5(3), 154-161. doi: 10.11648/j.ajtas.20160503.21

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AMA Style

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. Am J Theor Appl Stat. 2016;5(3):154-161. doi: 10.11648/j.ajtas.20160503.21

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@article{10.11648/j.ajtas.20160503.21,
  author = {Wafula Mike Erick and Kemei Anderson Kimutai and Edward Gachangi Njenga},
  title = {Parameter Estimation of Kumaraswamy Distribution Based on Progressive Type II Censoring Scheme Using Expectation-Maximization Algorithm},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {3},
  pages = {154-161},
  doi = {10.11648/j.ajtas.20160503.21},
  url = {https://doi.org/10.11648/j.ajtas.20160503.21},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160503.21},
  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.},
 year = {2016}
}

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TY  - JOUR
T1  - Parameter Estimation of Kumaraswamy Distribution Based on Progressive Type II Censoring Scheme Using Expectation-Maximization Algorithm
AU  - Wafula Mike Erick
AU  - Kemei Anderson Kimutai
AU  - Edward Gachangi Njenga
Y1  - 2016/06/01
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160503.21
DO  - 10.11648/j.ajtas.20160503.21
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 154
EP  - 161
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160503.21
AB  - 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.
VL  - 5
IS  - 3
ER  -

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Author Information

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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Plain Text BibTeX RIS

APA Style

Wafula Mike Erick, Kemei Anderson Kimutai, Edward Gachangi Njenga. (2016). Parameter Estimation of Kumaraswamy Distribution Based on Progressive Type II Censoring Scheme Using Expectation-Maximization Algorithm. American Journal of Theoretical and Applied Statistics, 5(3), 154-161. https://doi.org/10.11648/j.ajtas.20160503.21

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ACS Style

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. Am. J. Theor. Appl. Stat. 2016, 5(3), 154-161. doi: 10.11648/j.ajtas.20160503.21

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AMA Style

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. Am J Theor Appl Stat. 2016;5(3):154-161. doi: 10.11648/j.ajtas.20160503.21

Copy | Download

@article{10.11648/j.ajtas.20160503.21,
  author = {Wafula Mike Erick and Kemei Anderson Kimutai and Edward Gachangi Njenga},
  title = {Parameter Estimation of Kumaraswamy Distribution Based on Progressive Type II Censoring Scheme Using Expectation-Maximization Algorithm},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {3},
  pages = {154-161},
  doi = {10.11648/j.ajtas.20160503.21},
  url = {https://doi.org/10.11648/j.ajtas.20160503.21},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160503.21},
  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.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Parameter Estimation of Kumaraswamy Distribution Based on Progressive Type II Censoring Scheme Using Expectation-Maximization Algorithm
AU  - Wafula Mike Erick
AU  - Kemei Anderson Kimutai
AU  - Edward Gachangi Njenga
Y1  - 2016/06/01
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160503.21
DO  - 10.11648/j.ajtas.20160503.21
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 154
EP  - 161
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160503.21
AB  - 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.
VL  - 5
IS  - 3
ER  -

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