A Bayesian Analysis and Estimation of Weibull Inverse Rayleigh Distribution Using HMC Method

Abstract

Under the Bayesian environment we have analyzed the Weibull inverse Rayleigh model. The parameters of the model are estimated and predicted through posterior samples which are generated using Markov Chain Monte Carlo (MCMC) technique. The concern model is fitted using Stan software (a probabilistic programming language), utilizing the Hamiltonian Monte Carlo (HMC) algorithm and its adaptive variant the No-U-turn sampler (NUTS). For the illustration, we have considered a real data set and performed Bayesian analysis numerically and graphically using weakly Gamma informative priors. The posterior predictive check is also carried out to accesses the predictability of the model. The tools and methods used in this article are under the Bayesian approach which is implemented in R statistical programming language.