Extended Bayesian Analysis through Wrapped Distribution: Illustrated with the Posterior Wrapped Exponential Distribution

Mangkon  Damnet; Amornrat  Suriyawichitseranee; Jessada  Tanthanuch

Authors

Mangkon Damnet School of Mathematical Sciences and Geoinformatics, Institution Science, Suranaree University of Technology, Nakhon Ratchasima, Thailand
Amornrat Suriyawichitseranee School of Mathematical Sciences and Geoinformatics, Institution Science, Suranaree University of Technology, Nakhon Ratchasima, Thailand
Jessada Tanthanuch School of Mathematical Sciences and Geoinformatics, Institution Science, Suranaree University of Technology, Nakhon Ratchasima, Thailand

Keywords:

Wrapped distribution, posterior wrapped exponential distribution, Bayesian estimator, minimal posterior expected losses

Abstract

This article explores the extension of Bayesian analysis through wrapped distributions. The study introduces the concept of posterior wrapped distributions derived under both uninformative and informative (gamma distribution) priors to obtain the posterior wrapped exponential distributions. Statistical measures such as mean, variance, skewness, kurtosis, and moment generating functions of the distributions are presented. Bayesian estimators and minimal posterior expected losses for the obtained distributions are derived. The probability density functions curves and their statistical properties are also investigated. Additionally, two examples of utilizing the posterior wrapped exponential distributions in real-life situations are demonstrated.

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