Application of Progressive Type II Hybrid Censoring Scheme to Estimate Parameters of Kumaraswamy Distribution

Meymuna Shariff Jaffer; Edward Gachangi Njenga; George Kemboi Kirui Keitany

doi:doi:10.11648/j.ajtas.20221106.12

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Application of Progressive Type II Hybrid Censoring Scheme to Estimate Parameters of Kumaraswamy Distribution

Meymuna Shariff Jaffer, Edward Gachangi Njenga, George Kemboi Kirui Keitany

Published in American Journal of Theoretical and Applied Statistics (Volume 11, Issue 6)

Received: 22 October 2022 Accepted: 7 November 2022 Published: 11 November 2022

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Abstract

This paper considers the Maximum Likelihood Estimators for Kumaraswamy distribution centered on progressive type II hybrid censoring scheme using the expectation maximization algorithm. Kumaraswamy distribution remains of keen consideration in disciplines such as economics, hydrology and survival analysis. To compare the performance of the attained maximum likelihood estimators of Kumaraswamy distribution expectation maximization algorithms is utilized as it is a convenient mechanism in manipulating incomplete data. The presentation of the maximum likelihood estimators via an expectation maximization algorithm is compared using three different amalgamations of censoring schemes. Simulation is utilized to contrast both precision and efficiency. The simulation outcome indicates that there is no notable estimation difference for the three censoring schemes. It also noted that an expectation maximization algorithm has a relatively efficient estimation aimed at Kumaraswamy distribution in progressive type II hybrid censoring scheme. Eventually, an illustration with real life data set is provided and it illustrates how maximum likelihood estimators works in practice under different censoring schemes. It is apparent from the observations made that the estimated values in scheme one is lesser than the other remaining two censoring schemes. It is greater in scheme three than scheme one and scheme two whenever, the three schemes are compared.

Published in	American Journal of Theoretical and Applied Statistics (Volume 11, Issue 6)
DOI	10.11648/j.ajtas.20221106.12
Page(s)	175-183
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), 2024. Published by Science Publishing Group

Keywords

Kumaraswamy Distribution, Progressive Type II Hybrid Censoring, Maximum Likelihood Estimators, Expectation Maximization Algorithm

References

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[2]	Childs, A., Chandrasekar, B., and Balakrishnan, N. (2008). Exact likelihood Inference for An Ex-ponential Parameter Under Progressive Hybrid Censoring Schemes." In Statistical Models and Methods for Biomedical and Technical Systems, pp. 319 {330. Springer.
[3]	Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society, B; 39: 1-39.
[4]	El-Sagheer, R., (2015). Estimating parameters of Kumaraswamy distribution using progressively censored data. Journal of testing and evaluation. https://doi.org/10.1520/jte20150393. ISSN 0090-3973.
[5]	Epstein, B. (1954). Truncated life tests in the exponential case. Annals of Mathematical Statistics, 25, 555-564.
[6]	Gholizadeh, R., Khalilpor, M., and Hadian, M. (2011). Bayesian estimations in the Kumaraswaamy distribution under progressively type II censoring data. International journal of engineering, science and technology, vol. 3, No. 9, pp 47-65.
[7]	Kumaraswamy, P., (1980). Generalized probability density-function for double-bounded random-processes. J Hydrol 46, 79–88.
[8]	Kundu, D., and Joarder, A. (2006). Analysis of Type II progressively hybrid censored data. Comput. stat. Data Anal, 50, pp 2509-2528.
[9]	Li, J., and Lina, M. (2015). Inference for the Generalized Rayleigh Distribution Based on Progressively Type II hybrid Censored data. Journal of Information and Computational Science, 1101-1112.
[10]	Lin, C. T., Ng, H. K. T., and Chan, P. S. (2009), “Statistical inference of Type-II progressively hybrid censored data with Weibull lifetimes,” Communications in Statistics – Theory and Methods, vol. 38, 1710-1729.
[11]	Mokhtari, E. B., Rad, A. H. and Yousefzadeh, F. (2011). Inference for Weibull distribution based on progressively type II hybrid censored data. Journal of Statistical Planning and Inference, 141 (8), 2824-2838.
[12]	Muna, S. (2017). Comparing different estimators of two parameters Kumaraswamy distribution. Journal of Babylon University/ pure and applied sciences No (2) vol. (25).
[13]	Ng, H. K. T., Chan, C. S., and Balakrishnan, N. (2002). Estimation of Parameters from Progressively Censored Data Using EM algorithm. Computational Statistics and Data Analysis, 39, 371-386.
[14]	Pak, A., Mahmoudi, M. R., and Rastogi, M. K., (2018). Classical and Bayesian estimation of Kumaraswamy distribution based on type II hybrid censored data. Electronic journal of Applied statistical analysis vol. 11, issue 01, 235-252.
[15]	Park, S., Balakrishnan, N., and Kim, S. (2011). Fisher information in progressive hybrid censoring schemes. A journal of theoretical and applied statistic. Volume 45, 2011-issue 6.
[16]	Sultan, H., and Ahmad, S. P. (2015). Bayesian approximation techniques for Kumaraswamy distribution. Mathematical theory and modeling ISSN 2224-5804 vol 5, No 5.
[17]	Sultana, F., Mani, Y., Kumar, M., and Wu, S. (2018). Parameter estimation for the Kumaraswamy distribution based on hybrid censoring. American journal of mathematical and management sciences, Vol 37, issue 3.
[18]	Yongming, M., and Yimin, S., (2013). Inference for lomax distribution based on type II progressively hybrid censored data. Journal of physical sciences, vol. 17, 2013, 33-41.

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Meymuna Shariff Jaffer, Edward Gachangi Njenga, George Kemboi Kirui Keitany. (2022). Application of Progressive Type II Hybrid Censoring Scheme to Estimate Parameters of Kumaraswamy Distribution. American Journal of Theoretical and Applied Statistics, 11(6), 175-183. https://doi.org/10.11648/j.ajtas.20221106.12

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Meymuna Shariff Jaffer; Edward Gachangi Njenga; George Kemboi Kirui Keitany. Application of Progressive Type II Hybrid Censoring Scheme to Estimate Parameters of Kumaraswamy Distribution. Am. J. Theor. Appl. Stat. 2022, 11(6), 175-183. doi: 10.11648/j.ajtas.20221106.12

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AMA Style

Meymuna Shariff Jaffer, Edward Gachangi Njenga, George Kemboi Kirui Keitany. Application of Progressive Type II Hybrid Censoring Scheme to Estimate Parameters of Kumaraswamy Distribution. Am J Theor Appl Stat. 2022;11(6):175-183. doi: 10.11648/j.ajtas.20221106.12

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@article{10.11648/j.ajtas.20221106.12,
  author = {Meymuna Shariff Jaffer and Edward Gachangi Njenga and George Kemboi Kirui Keitany},
  title = {Application of Progressive Type II Hybrid Censoring Scheme to Estimate Parameters of Kumaraswamy Distribution},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {11},
  number = {6},
  pages = {175-183},
  doi = {10.11648/j.ajtas.20221106.12},
  url = {https://doi.org/10.11648/j.ajtas.20221106.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20221106.12},
  abstract = {This paper considers the Maximum Likelihood Estimators for Kumaraswamy distribution centered on progressive type II hybrid censoring scheme using the expectation maximization algorithm. Kumaraswamy distribution remains of keen consideration in disciplines such as economics, hydrology and survival analysis. To compare the performance of the attained maximum likelihood estimators of Kumaraswamy distribution expectation maximization algorithms is utilized as it is a convenient mechanism in manipulating incomplete data. The presentation of the maximum likelihood estimators via an expectation maximization algorithm is compared using three different amalgamations of censoring schemes. Simulation is utilized to contrast both precision and efficiency. The simulation outcome indicates that there is no notable estimation difference for the three censoring schemes. It also noted that an expectation maximization algorithm has a relatively efficient estimation aimed at Kumaraswamy distribution in progressive type II hybrid censoring scheme. Eventually, an illustration with real life data set is provided and it illustrates how maximum likelihood estimators works in practice under different censoring schemes. It is apparent from the observations made that the estimated values in scheme one is lesser than the other remaining two censoring schemes. It is greater in scheme three than scheme one and scheme two whenever, the three schemes are compared.},
 year = {2022}
}

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TY  - JOUR
T1  - Application of Progressive Type II Hybrid Censoring Scheme to Estimate Parameters of Kumaraswamy Distribution
AU  - Meymuna Shariff Jaffer
AU  - Edward Gachangi Njenga
AU  - George Kemboi Kirui Keitany
Y1  - 2022/11/11
PY  - 2022
N1  - https://doi.org/10.11648/j.ajtas.20221106.12
DO  - 10.11648/j.ajtas.20221106.12
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  - 175
EP  - 183
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20221106.12
AB  - This paper considers the Maximum Likelihood Estimators for Kumaraswamy distribution centered on progressive type II hybrid censoring scheme using the expectation maximization algorithm. Kumaraswamy distribution remains of keen consideration in disciplines such as economics, hydrology and survival analysis. To compare the performance of the attained maximum likelihood estimators of Kumaraswamy distribution expectation maximization algorithms is utilized as it is a convenient mechanism in manipulating incomplete data. The presentation of the maximum likelihood estimators via an expectation maximization algorithm is compared using three different amalgamations of censoring schemes. Simulation is utilized to contrast both precision and efficiency. The simulation outcome indicates that there is no notable estimation difference for the three censoring schemes. It also noted that an expectation maximization algorithm has a relatively efficient estimation aimed at Kumaraswamy distribution in progressive type II hybrid censoring scheme. Eventually, an illustration with real life data set is provided and it illustrates how maximum likelihood estimators works in practice under different censoring schemes. It is apparent from the observations made that the estimated values in scheme one is lesser than the other remaining two censoring schemes. It is greater in scheme three than scheme one and scheme two whenever, the three schemes are compared.
VL  - 11
IS  - 6
ER  -

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Author Information

Meymuna Shariff Jaffer

Department of Mathematics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya
Edward Gachangi Njenga

Department of Mathematics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya
George Kemboi Kirui Keitany

Department of Mathematics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya

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APA Style

Meymuna Shariff Jaffer, Edward Gachangi Njenga, George Kemboi Kirui Keitany. (2022). Application of Progressive Type II Hybrid Censoring Scheme to Estimate Parameters of Kumaraswamy Distribution. American Journal of Theoretical and Applied Statistics, 11(6), 175-183. https://doi.org/10.11648/j.ajtas.20221106.12

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ACS Style

Meymuna Shariff Jaffer; Edward Gachangi Njenga; George Kemboi Kirui Keitany. Application of Progressive Type II Hybrid Censoring Scheme to Estimate Parameters of Kumaraswamy Distribution. Am. J. Theor. Appl. Stat. 2022, 11(6), 175-183. doi: 10.11648/j.ajtas.20221106.12

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AMA Style

Meymuna Shariff Jaffer, Edward Gachangi Njenga, George Kemboi Kirui Keitany. Application of Progressive Type II Hybrid Censoring Scheme to Estimate Parameters of Kumaraswamy Distribution. Am J Theor Appl Stat. 2022;11(6):175-183. doi: 10.11648/j.ajtas.20221106.12

Copy | Download

@article{10.11648/j.ajtas.20221106.12,
  author = {Meymuna Shariff Jaffer and Edward Gachangi Njenga and George Kemboi Kirui Keitany},
  title = {Application of Progressive Type II Hybrid Censoring Scheme to Estimate Parameters of Kumaraswamy Distribution},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {11},
  number = {6},
  pages = {175-183},
  doi = {10.11648/j.ajtas.20221106.12},
  url = {https://doi.org/10.11648/j.ajtas.20221106.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20221106.12},
  abstract = {This paper considers the Maximum Likelihood Estimators for Kumaraswamy distribution centered on progressive type II hybrid censoring scheme using the expectation maximization algorithm. Kumaraswamy distribution remains of keen consideration in disciplines such as economics, hydrology and survival analysis. To compare the performance of the attained maximum likelihood estimators of Kumaraswamy distribution expectation maximization algorithms is utilized as it is a convenient mechanism in manipulating incomplete data. The presentation of the maximum likelihood estimators via an expectation maximization algorithm is compared using three different amalgamations of censoring schemes. Simulation is utilized to contrast both precision and efficiency. The simulation outcome indicates that there is no notable estimation difference for the three censoring schemes. It also noted that an expectation maximization algorithm has a relatively efficient estimation aimed at Kumaraswamy distribution in progressive type II hybrid censoring scheme. Eventually, an illustration with real life data set is provided and it illustrates how maximum likelihood estimators works in practice under different censoring schemes. It is apparent from the observations made that the estimated values in scheme one is lesser than the other remaining two censoring schemes. It is greater in scheme three than scheme one and scheme two whenever, the three schemes are compared.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Application of Progressive Type II Hybrid Censoring Scheme to Estimate Parameters of Kumaraswamy Distribution
AU  - Meymuna Shariff Jaffer
AU  - Edward Gachangi Njenga
AU  - George Kemboi Kirui Keitany
Y1  - 2022/11/11
PY  - 2022
N1  - https://doi.org/10.11648/j.ajtas.20221106.12
DO  - 10.11648/j.ajtas.20221106.12
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  - 175
EP  - 183
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20221106.12
AB  - This paper considers the Maximum Likelihood Estimators for Kumaraswamy distribution centered on progressive type II hybrid censoring scheme using the expectation maximization algorithm. Kumaraswamy distribution remains of keen consideration in disciplines such as economics, hydrology and survival analysis. To compare the performance of the attained maximum likelihood estimators of Kumaraswamy distribution expectation maximization algorithms is utilized as it is a convenient mechanism in manipulating incomplete data. The presentation of the maximum likelihood estimators via an expectation maximization algorithm is compared using three different amalgamations of censoring schemes. Simulation is utilized to contrast both precision and efficiency. The simulation outcome indicates that there is no notable estimation difference for the three censoring schemes. It also noted that an expectation maximization algorithm has a relatively efficient estimation aimed at Kumaraswamy distribution in progressive type II hybrid censoring scheme. Eventually, an illustration with real life data set is provided and it illustrates how maximum likelihood estimators works in practice under different censoring schemes. It is apparent from the observations made that the estimated values in scheme one is lesser than the other remaining two censoring schemes. It is greater in scheme three than scheme one and scheme two whenever, the three schemes are compared.
VL  - 11
IS  - 6
ER  -

Copy | Download