Abstract
Models with bathtub-shaped hazard function have been widely accepted in the field of reliability and medicine and are particularly useful in reliability related decision making and cost analysis. In this paper, the exponential power model capable of assuming increasing as well as bathtub-shape, is studied. This article makes a Bayesian study of the same model and simultaneously shows how posterior simulations based on Markov chain Monte Carlo algorithms can be straightforward and routine in R. The study is carried out for complete as well as censored data, under the assumption of weakly-informative priors for the parameters. In addition to this, inference interest focuses on the posterior distribution of non-linear functions of the parameters. Also, the model has been extended to include continuous explanatory variables and R-codes are well illustrated. Two real data sets are considered for illustrative purposes.
Highlights
In reliability analysis, hazard rate plays an indispensable role to characterize life phenomena
This paper develops the Bayesian inference procedures for the exponential power model assuming weakly-informative priors for the model parameters
A distinguishing feature of this paper is that both the analytic and simulation-based Bayesian studies are conducted in R language using the package LaplacesDemon
Summary
Hazard rate plays an indispensable role to characterize life phenomena. The function LaplacesDemon Given data, a model specification, and initial values, LaplacesDemon maximizes the logarithm of the unnormalized joint posterior density with Markov chain Monte Carlo (MCMC) algorithms, called samplers, and provides samples of the marginal posterior distributions, deviance and other monitored variables.
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