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

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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.

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Supplementary information

Codes (written in R) for calculating MDPDEs and their standard errors, optimal tuning parameter selection, and model selection are provided in the Supplementary Material (also available at https://github.com/arnabstatswithR/robustrainfall.git). Tables of the best-fit models and the median rainfall amounts estimated based on the MDPDE from the best-fitted models are also provided.

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Acknowledgements

The authors would like to thank an Associate Editor and two anonymous reviewers for their several thoughtful suggestions which improved the flow and the content of the paper substantially. The research of the first author is partially supported by the Indian Institute of Technology Kanpur and Rice University collaborative research grant under Award No. DOIR/2023246.

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  1. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, 208016, India

    Arnab Hazra

  2. Interdisciplinary Statistical Research Unit, Indian Statistical Institute, Kolkata, 208016, India

    Abhik Ghosh

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  1. Arnab Hazra
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Hazra, A., Ghosh, A. Robust Statistical Modeling of Monthly Rainfall: The Minimum Density Power Divergence Approach. Sankhya B 86, 241–279 (2024). https://doi.org/10.1007/s13571-024-00324-0

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