Parameter Estimation on the Asymptotic Distribution of the Maximum Daily Rainfall of Wet Periods in the Northeast Thailand

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Abstract
In this paper, we continue investigation on modeling the extreme values of daily rainfall (an amount of unusually heavy rain). The tempered Snedecor–Fisher distribution was suggested as the asymptotic distribution of the maximum daily rainfall during the sequence of wet days in the literature. One of the parameters of the tempered Snedecor–Fisher distribution is related to the distribution of the number of wet days, which can be modeled by the negative binomial distribution. Our study shows the effectiveness of fitting the number of consecutive rainy days by the zero-truncated negative binomial distribution. Estimating the parameter using the EM algorithm yields the asymptotic approximation distribution that closely mirrors the empirical distribution of maximum daily rainfall compared to traditional moment and maximum likelihood methods, which were fitted by classical shifted negative binomial distribution. This enhances the reliability of the criteria employed to identify thresholds for abnormal daily rainfall values.

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