Robust statistical modeling of monthly rainfall: The minimum density power divergence approach

TL;DR

This paper introduces a robust statistical method using minimum density power divergence estimation to model monthly rainfall data, effectively handling outliers and improving fit over traditional maximum likelihood approaches.

Contribution

It proposes and demonstrates a robust parameter estimation technique for rainfall models, outperforming MLE especially in the presence of outliers, with application to Indian meteorological data.

Findings

MDPDE provides more reliable parameter estimates than MLE.

Robust models better fit rainfall data with outliers.

Application to Indian data shows improved model performance.

Abstract

Statistical modeling of monthly, seasonal, or annual rainfall data is an important research area in meteorology. These models play a crucial role in rainfed agriculture, where a proper assessment of the future availability of rainwater is necessary. The rainfall amount during a rainy month or a whole rainy season} can take any positive value and some simple (one or two-parameter) probability models supported over the positive real line that are generally used for rainfall modeling are exponential, gamma, Weibull, lognormal, Pearson Type-V/VI, log-logistic, etc., where the unknown model parameters are routinely estimated using the maximum likelihood estimator (MLE). However, the presence of outliers or extreme observations is a common issue in rainfall data and the MLEs being highly sensitive to them often leads to spurious inference. Here, we discuss a robust parameter estimation approach based on the minimum density power divergence estimator (MDPDE). We fit the above four parametric models to the detrended areally-weighted monthly rainfall data from the 36 meteorological subdivisions of India for the years 1951-2014 and compare the fits based on MLE and the proposed optimum MDPDE; the superior performance of MDPDE is showcased for several cases. For all month-subdivision combinations, we discuss the best-fit models and median rainfall amounts.