On the bimodal Gumbel model with application to environmental data

TL;DR

This paper introduces a bimodal generalization of the Gumbel distribution, providing new analytical properties, estimation methods, and an application to real environmental data, expanding modeling capabilities for bimodal datasets.

Contribution

The paper presents a novel bimodal Gumbel distribution, deriving its properties, estimation techniques, and demonstrating its applicability to environmental data.

Findings

Derived the probability density and hazard rate functions.

Verified properties using Markov chain Monte Carlo simulations.

Applied the model successfully to real environmental data.

Abstract

The Gumbel model is a very popular statistical model due to its wide applicability for instance in the course of certain survival, environmental, financial or reliability studies. In this work, we have introduced a bimodal generalization of the Gumbel distribution that can be an alternative to model bimodal data. We derive the analytical shapes of the corresponding probability density function and the hazard rate function and provide graphical illustrations. Furthermore, We have discussed the properties of this density such as mode, bimodality, moment generating function and moments. Our results were verified using the Markov chain Monte Carlo simulation method. The maximum likelihood method is used for parameters estimation. Finally, we also carry out an application to real data that demonstrates the usefulness of the proposed distribution.