Robust Assessing the Lifetime Performance of Products with Inverse Gaussian Distribution in Bayesian and Classical Setup

Abstract

The inverse Gaussian (Wald) distribution belongs to the two-parameter family of continuous distributions having a range from 0 to ∞ and is considered as a potential candidate to model diffusion processes and lifetime datasets. Bayesian analysis is a modern inferential technique in which we estimate the parameters of the posterior distribution obtained by formally combining a prior distribution with an observed data distribution. In this article, we have attempted to perform the Bayesian and classical analyses of the Wald distribution and compare the results. Jeffreys' and uniform priors are used as noninformative priors, while the exponential distribution is used as an informative prior. The analysis comprises finding joint posterior distributions, the posterior means, predictive distributions, and credible intervals. To illustrate the entire estimation procedure, we have used real and simulated datasets, and the results thus obtained are discussed and compared. We have used the Bayesian specialized Open BUGS software to perform Markov Chain Monte Carlo (MCMC) simulations using a real dataset.

Developing Bayesian EWMA chart for change detection in the shape parameter of Inverse Gaussian process

“…Ali [24] introduced Bayesian predictive monitoring of time between events. The Bayesian setup has also been studied in [22,[25][26][27][28][29][30][31][32][33][34][35]. Jones et al [36] reconfigured the CUSUM and EWMA CCs to monitor the process under the Bayesian approach.…”

On Testing the Adequacy of the Inverse Gaussian Distribution

“…The authors of [31] study Bayesian estimation of the parameters of the inverse Gaussian distribution and use Markov chain Monte Carlo techniques to implement these estimates. In [32] some inferential results for the inverse Gaussian distribution are derived by considering a proper prior distribution, while [33] performed Bayesian inference for the parameters of this distribution and compared the results with the classical maximum likelihood estimators.…”