Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Classical and Bayesian Estimation of Two-Parameter Power Function Distribution

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. Preprints 2021, 2021080222 (doi: 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 (doi: 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

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