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

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  • Arnab Hazra

    (Indian Institute of Technology Kanpur)

  • Abhik Ghosh

    (Indian Statistical Institute)

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.

Suggested Citation

  • Arnab Hazra & Abhik Ghosh, 2024. "Robust Statistical Modeling of Monthly Rainfall: The Minimum Density Power Divergence Approach," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(1), pages 241-279, May.
    • Handle: RePEc:spr:sankhb:v:86:y:2024:i:1:d:10.1007_s13571-024-00324-0
    DOI: 10.1007/s13571-024-00324-0
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