Classical and Bayesian Inference of the Inverse Nakagami Distribution Based on Progressive Type-II Censored Samples

Liang Wang, Sanku Dey and Yogesh Mani Tripathi
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Liang Wang: School of Mathematics, Yunnan Normal University, Kunming 650500, China
Sanku Dey: Department of Statistics, St. Anthony’s College, Shillong 793001, Meghalaya, India
Yogesh Mani Tripathi: Department of Mathematics, Indian Institute of Technology Patna, Patna 800013, Bihar, India

Mathematics, 2022, vol. 10, issue 12, 1-18

Abstract: This paper explores statistical inferences when the lifetime of product follows the inverse Nakagami distribution using progressive Type-II censored data. Likelihood-based and maximum product of spacing (MPS)-based methods are considered for estimating the parameters of the model. In addition, approximate confidence intervals are constructed via the asymptotic theory using both likelihood and product spacing functions. Based on traditional likelihood and the product of spacing functions, Bayesian estimates are also considered under a squared error loss function using non-informative priors, and Gibbs sampling based on the MCMC algorithm is proposed to approximate the Bayes estimates, where the highest posterior density credible intervals of the parameters are obtained. Numerical studies are presented to compare the proposed estimators using Monte Carlo simulations. To demonstrate the proposed methodology in a real-life scenario, a well-known data set on agricultural machine elevators with high defect rates is also analyzed for illustration.

Keywords: inverse Nakagami model; progressively censored data; maximum likelihood estimation; maximum product of spacing approach; Bayesian inference (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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