Robust Statistical Modeling of Monthly Rainfall: The Minimum Density Power Divergence Approach

Arnab Hazra () and Abhik Ghosh ()
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Arnab Hazra: Indian Institute of Technology Kanpur
Abhik Ghosh: Indian Statistical Institute

Sankhya B: The Indian Journal of Statistics, 2024, vol. 86, issue 1, No 10, 279 pages

Abstract: 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.

Keywords: Adjusted-Boxplot method; maximum likelihood estimation; minimum density power divergence estimation; outliers or extreme observations; subdivision-wise areally-weighted rainfall of India; Wasserstein distance (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13571-024-00324-0

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