Minimum Density Power Divergence Estimation for the Generalized Exponential Distribution

TL;DR

This paper introduces a robust parameter estimation method for the generalized exponential distribution using minimum density power divergence estimation, demonstrating improved performance over traditional methods in rainfall data analysis.

Contribution

The paper develops and analytically compares a robust estimation technique for the generalized exponential distribution, including its asymptotic properties and influence function analysis.

Findings

MDPDE provides more robust estimates than MLE in rainfall datasets.

Analytical expressions for estimating equations and asymptotic distributions are derived.

Simulation and real data applications show superior performance of MDPDE.

Abstract

Statistical modeling of rainfall data is an active research area in agro-meteorology. The most common models fitted to such datasets are exponential, gamma, log-normal, and Weibull distributions. As an alternative to some of these models, the generalized exponential (GE) distribution was proposed by Gupta and Kundu (2001, Exponentiated Exponential Family: An Alternative to Gamma and Weibull Distributions, Biometrical Journal). Rainfall (specifically for short periods) datasets often include outliers, and thus, a proper robust parameter estimation procedure is necessary. Here, we use the popular minimum density power divergence estimation (MDPDE) procedure developed by Basu et al. (1998, Robust and Efficient Estimation by Minimising a Density Power Divergence, Biometrika) for estimating the GE parameters. We derive the analytical expressions for the estimating equations and asymptotic distributions. We analytically compare MDPDE with maximum likelihood estimation in terms of robustness, through an influence function analysis. Besides, we study the asymptotic relative efficiency of MDPDE analytically for different parameter settings. We apply the proposed technique to some simulated datasets and two rainfall datasets from Texas, United States. The results indicate superior performance of MDPDE compared to the other existing estimation techniques in most of the scenarios.