Transmuted Generalized Inverse Weibull Distribution

TL;DR

This paper introduces a transmuted version of the generalized inverse Weibull distribution, enhancing its flexibility with a new parameter, and derives its properties, estimation methods, and demonstrates its effectiveness on real data.

Contribution

It proposes the transmuted generalized inverse Weibull distribution using QRTM, providing explicit properties and estimation methods, and compares its flexibility to the original distribution.

Findings

The transmuted distribution offers increased flexibility.

Explicit formulas for moments, quantiles, and MGF are derived.

Real data application shows improved fit over the original distribution.

Abstract

A generalization of the generalized inverse Weibull distribution so-called transmuted generalized inverse Weibull dis- tribution is proposed and studied. We will use the quadratic rank transmutation map (QRTM) in order to generate a flexible family of probability distributions taking generalized inverse Weibull distribution as the base value distribution by introducing a new parameter that would offer more distributional flexibility. Various structural properties including explicit expressions for the mo- ments, quantiles, and moment generating function of the new dis- tribution are derived.We proposed the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set are used to compare the exibility of the transmuted version versus the generalized inverseWeibull distribution.