A weighted transmuted exponential distribution with environmental applications

TL;DR

This paper introduces a new three-parameter distribution combining re-parametrized EGNB2 and transmuted exponential distributions, enhancing flexibility for modeling environmental data and analyzing its properties and fit.

Contribution

It proposes a novel distribution with added parameters for better modeling flexibility, explores its mathematical properties, and demonstrates its superior fit to environmental data.

Findings

Distribution shows improved fit over existing models

Mathematical properties like hazard rate and moments are derived

Distribution effectively estimates environmental measures

Abstract

In this paper, we introduce a new three-parameter distribution based on the combination of re-parametrization of the so-called EGNB2 and transmuted exponential distributions. This combination aims to modify the transmuted exponential distribution via the incorporation of an additional parameter, mainly adding a high degree of flexibility on the mode and impacting the skewness and kurtosis of the tail. We explore some mathematical properties of this distribution including the hazard rate function, moments, the moment generating function, the quantile function, various entropy measures and (reversed) residual life functions. A statistical study investigates estimation of the parameters using the method of maximum likelihood. The distribution along with other existing distributions are fitted to two environmental data sets and its superior performance is assessed by using some goodness-of-fit tests. As a result, some environmental measures associated with these data are obtained such as the return level and mean deviation about this level.