Estimation of the Parameters of Poisson-Exponential Distribution Based on Progressively Type II Censoring Using the Expectation Maximization (Em) Algorithm

Joseph Nderitu Gitahi; John Kung’u; Leo Odongo

doi:doi:10.11648/j.ajtas.20170603.12

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Estimation of the Parameters of Poisson-Exponential Distribution Based on Progressively Type II Censoring Using the Expectation Maximization (Em) Algorithm

Joseph Nderitu Gitahi, John Kung’u, Leo Odongo

Published in American Journal of Theoretical and Applied Statistics (Volume 6, Issue 3)

Received: 16 March 2017 Accepted: 6 April 2017 Published: 27 April 2017

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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.

Published in	American Journal of Theoretical and Applied Statistics (Volume 6, Issue 3)
DOI	10.11648/j.ajtas.20170603.12
Page(s)	141-149
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), 2017. Published by Science Publishing Group

Keywords

Poisson-Exponential Distribution, Progressive Type II Censoring, Maximum Likelihood Estimation, EM Algorithm

References

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APA Style

Joseph Nderitu Gitahi, John Kung’u, Leo Odongo. (2017). 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, 6(3), 141-149. https://doi.org/10.11648/j.ajtas.20170603.12

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ACS Style

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. Am. J. Theor. Appl. Stat. 2017, 6(3), 141-149. doi: 10.11648/j.ajtas.20170603.12

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AMA Style

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. Am J Theor Appl Stat. 2017;6(3):141-149. doi: 10.11648/j.ajtas.20170603.12

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@article{10.11648/j.ajtas.20170603.12,
  author = {Joseph Nderitu Gitahi and John Kung’u and Leo Odongo},
  title = {Estimation of the Parameters of Poisson-Exponential Distribution Based on Progressively Type II Censoring Using the Expectation Maximization (Em) Algorithm},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {6},
  number = {3},
  pages = {141-149},
  doi = {10.11648/j.ajtas.20170603.12},
  url = {https://doi.org/10.11648/j.ajtas.20170603.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170603.12},
  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.},
 year = {2017}
}

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TY  - JOUR
T1  - Estimation of the Parameters of Poisson-Exponential Distribution Based on Progressively Type II Censoring Using the Expectation Maximization (Em) Algorithm
AU  - Joseph Nderitu Gitahi
AU  - John Kung’u
AU  - Leo Odongo
Y1  - 2017/04/27
PY  - 2017
N1  - https://doi.org/10.11648/j.ajtas.20170603.12
DO  - 10.11648/j.ajtas.20170603.12
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  - 141
EP  - 149
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20170603.12
AB  - 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.
VL  - 6
IS  - 3
ER  -

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Author Information

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

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Plain Text BibTeX RIS

APA Style

Joseph Nderitu Gitahi, John Kung’u, Leo Odongo. (2017). 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, 6(3), 141-149. https://doi.org/10.11648/j.ajtas.20170603.12

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ACS Style

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. Am. J. Theor. Appl. Stat. 2017, 6(3), 141-149. doi: 10.11648/j.ajtas.20170603.12

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AMA Style

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. Am J Theor Appl Stat. 2017;6(3):141-149. doi: 10.11648/j.ajtas.20170603.12

Copy | Download

@article{10.11648/j.ajtas.20170603.12,
  author = {Joseph Nderitu Gitahi and John Kung’u and Leo Odongo},
  title = {Estimation of the Parameters of Poisson-Exponential Distribution Based on Progressively Type II Censoring Using the Expectation Maximization (Em) Algorithm},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {6},
  number = {3},
  pages = {141-149},
  doi = {10.11648/j.ajtas.20170603.12},
  url = {https://doi.org/10.11648/j.ajtas.20170603.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170603.12},
  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.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Estimation of the Parameters of Poisson-Exponential Distribution Based on Progressively Type II Censoring Using the Expectation Maximization (Em) Algorithm
AU  - Joseph Nderitu Gitahi
AU  - John Kung’u
AU  - Leo Odongo
Y1  - 2017/04/27
PY  - 2017
N1  - https://doi.org/10.11648/j.ajtas.20170603.12
DO  - 10.11648/j.ajtas.20170603.12
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  - 141
EP  - 149
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20170603.12
AB  - 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.
VL  - 6
IS  - 3
ER  -

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