Abstract
In this paper, we provide an entropy inference method that is based on an objective Bayesian approach for upper record values having a two-parameter logistic distribution. We derive the entropy that is based on the i-th upper record value and the joint entropy that is based on the upper record values. Moreover, we examine their properties. For objective Bayesian analysis, we obtain objective priors, namely, the Jeffreys and reference priors, for the unknown parameters of the logistic distribution. The priors are based on upper record values. Then, we develop an entropy inference method that is based on these objective priors. In real data analysis, we assess the quality of the proposed models under the objective priors and compare them with the model under the informative prior.
Highlights
Shannon [1] proposed information theory for quantifying information loss and introduced statistical entropy
Approximate maximum likelihood estimators (MLE) (AMLE), derived estimators of the entropy of a double-exponential distribution that are based on multiply Type-II censored samples
We provide an entropy inference method that is based on an objective Bayesian approach for upper record values having the two-parameter logistic distribution
Summary
Shannon [1] proposed information theory for quantifying information loss and introduced statistical entropy. Baratpour et al [2] obtained the entropy of a continuous probability distribution using upper record values. Approximate MLE (AMLE), derived estimators of the entropy of a double-exponential distribution that are based on multiply Type-II censored samples. Seo and Kang [5], using estimators of the shape parameter in the generalized half-logistic distribution, developed methods for estimating entropy that are based on Type-II censored samples. We provide an entropy inference method that is based on an objective Bayesian approach for upper record values having the two-parameter logistic distribution. The paper is organized as follows: In Section 2, we obtain the Jeffreys and reference priors and derive an entropy inference method that is based on the two non-informative priors.
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