Bayesian Estimation of a Shape Parameter of a Weibull-Lomax Distribution Using Non-Informative Priors

Abstract

The Weibull-Lomax Distribution has several applications in the areas of sur-vival analysis, especially where survival chances of an event decrease with time. It has positive skewness and has been found to perform better than most family of Lomax distributions such as Lomax, Gamma-Lomax, Beta-Lomax, exponenciated-Lomax distributions. In this study, the shape parameter of the Weibull-Lomax Distribution is estimated using the Bayesian approach under two non-informative prior distributions. The non-informative priors considered are the Uniform and Jeffrey’s prior distributions. The squared error loss function (SELF), Quadratic loss function (QLF) and precautionary loss function (PLF) are used to derive the Bayesian estimators under each prior. the posterior distribution of the shape parameter of the Weibull-Lomax distribution . Furthermore, using simulation studies, the estimates are compared with the classical method (such as maximum likelihood) by employing biases and Mean Square Errors (MSEs). The result shows the Bayesian approach using Quadratic Loss Function (QLF) under both Uniform and Jeffrey’s priors produced the best estimates for the shape parameter.