Open AccessBayesian Estimation of the Parameters of the Odd Generalized Exponentiated - Inverse Exponential Distribution (OGE -IED)
Author(s) -
Treng Kirnan Gayus,
Sani I. Doguwa
Publication year - 2022
Publication title -
asian journal of probability and statistics
Language(s) - English
Resource type - Journals
ISSN - 2582-0230
DOI - 10.9734/ajpas/2022/v16i230399
Subject(s) - mathematics , exponential family , statistics , posterior predictive distribution , gamma distribution , exponential distribution , bayesian probability , marginal likelihood , exponential function , posterior probability , bayes estimator , bayesian linear regression , likelihood function , maximum likelihood , bayesian inference , mathematical analysis
The Odd Generalized Exponentiated-Inverse Exponential Distribution, a three parameter distribution, is a hybrid of the Generalized Exponential distribution. Each of the parameters were assigned a gamma prior independently resulting to a posterior distribution that is mathematically intractable impossible to obtain marginal posterior distribution for two of the parameters, and a likelihood function that is not known traditionally to R or other statistical software. Resort was made to STAN in order to obtain Bayesian estimates - leveraging on STAN’s provision for user-defined distribution functions. Two datasets were used; remission times (in months) of bladder cancer patients and COVID-19 Survey data in Andalusia, Spain. In the end, the Maximum Likelihood estimates maximized the likelihood more than the Bayesian estimates - though with a slight margin of not more than 0.77. On the other hand, the Bayesian estimates proved to be more stable yielding very negligible standard errors compared to the Maximum Likelihood estimates.