Bayesian Estimation of the Kumaraswamy Inverse Weibull Distribution

TL;DR

This paper introduces a three-parameter Bayesian model for the Kumaraswamy Inverse Weibull distribution, detailing its mathematical properties and applying it to real data for reliability analysis.

Contribution

It provides a comprehensive mathematical and Bayesian framework for the Kumaraswamy Inverse Weibull distribution, including properties, moments, and real data application.

Findings

Distribution models unimodal failure rates

Derived moments and generating functions

Applied Bayesian estimation to real data

Abstract

The Kumaraswamy Inverse Weibull distribution has the ability to model failure rates that have unimodal shapes and are quite common in reliability and biological studies. The three-parameter Kumaraswamy Inverse Weibull distribution with decreasing and unimodal failure rate is introduced. We provide a comprehensive treatment of the mathematical properties of the Kumaraswany Inverse Weibull distribution and derive expressions for its moment generating function and the $r$-th generalized moment. Some properties of the model with some graphs of density and hazard function are discussed. We also discuss a Bayesian approach for this distribution and an application was made for a real data set.