Version 1
: Received: 6 August 2021 / Approved: 10 August 2021 / Online: 10 August 2021 (09:54:48 CEST)
How to cite:
Liu, X.; Arslan, M.; Khan, M.; Anwar, S.M.; Rasheed, Z. Classical and Bayesian Estimation of Two-Parameter Power Function Distribution. Preprints2021, 2021080222. https://doi.org/10.20944/preprints202108.0222.v1
Liu, X.; Arslan, M.; Khan, M.; Anwar, S.M.; Rasheed, Z. Classical and Bayesian Estimation of Two-Parameter Power Function Distribution. Preprints 2021, 2021080222. https://doi.org/10.20944/preprints202108.0222.v1
Liu, X.; Arslan, M.; Khan, M.; Anwar, S.M.; Rasheed, Z. Classical and Bayesian Estimation of Two-Parameter Power Function Distribution. Preprints2021, 2021080222. https://doi.org/10.20944/preprints202108.0222.v1
APA Style
Liu, X., Arslan, M., Khan, M., Anwar, S.M., & Rasheed, Z. (2021). Classical and Bayesian Estimation of Two-Parameter Power Function Distribution. Preprints. https://doi.org/10.20944/preprints202108.0222.v1
Chicago/Turabian Style
Liu, X., Syed Masroor Anwar and Zahid Rasheed. 2021 "Classical and Bayesian Estimation of Two-Parameter Power Function Distribution" Preprints. https://doi.org/10.20944/preprints202108.0222.v1
Abstract
The power function distribution is a flexible waiting time model that may provide better fit for some failure data. This paper presents the comparison of the maximum likelihood estimates and the Bayes estimates of two-parameter power function distribution. The Bayes estimates are obtained, using conjugate priors, under five loss functions consist of square error, precautionary, weighted, LINEX and DeGroot loss function. The Gibbs sampling algorithm is proposed to generate samples from posterior distributions and in result the Bayes estimates are computed. The comparison of the maximum likelihood estimates and the Bayes estimates are done through the root mean squared errors. One real-life data set is analyzed to illustrate the evaluation of proposed methods of estimation. Finally, results from the simulation are discussed to assess the performance behavior of the maximum likelihood estimates and the Bayes estimates.
Keywords
Maximum likelihood estimate; Bayes estimate; Gamma distribution; Squared error loss function; Posterior distribution
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
