Property Of The Beta Modified Weibull Distribution With Six Parameters

TL;DR

This paper introduces a new six-parameter Beta Weibull distribution, generalizing existing models and capable of representing diverse hazard function shapes, supported by numerical simulations.

Contribution

The paper develops a new six-parameter Beta Weibull distribution that generalizes existing distributions and covers a wide range of hazard function shapes.

Findings

The new distribution's density function covers all shapes in literature.

Hazard functions include constant, increasing, decreasing, and complex shapes.

Numerical simulations confirm the distribution's flexibility.

Abstract

The aim of this article is to determine a new six-parameter Beta Weibull distribution and its various associated functions, namely the cumulative distribution, survival, probability density and hazard functions. Next, we determine the sub-distributions of the new distribution and show that the latter generalizes those of the literature. Finally, numerical simulations were performed and show that the shapes of the density function of the new distribution cover all those in the literature, and the shapes of hazard functions (constant, increasing, decreasing, $\bigcup$-shaped and $\bigcap$-shaped) are represented in the new distribution and encompass all existing distributions.