Abstract
In this study, Gaussian/normal distributions (N) and mixtures of two normal (N2), three normal (N3), four normal (N4), or five normal (N5) distributions were applied to data with extreme values for precipitation for 35 weather stations in Bangladesh. For parameter estimation, maximum likelihood estimation was applied by using an expectation-maximization algorithm. For selecting the best-fit model, graphical inspection (probability density function (pdf), cumulative density function (cdf), quantile-quantile (Q-Q) plot) and numerical criteria (Akaike’s information criterion (AIC), Bayesian information criterion (BIC), root mean square percentage error (RMSPE)) were used. In most of the cases, AIC and BIC gave the same best-fit results but their RMSPE results differed. The best-fit result of each station was chosen as the distribution with the lowest sum of the rank scores from each test statistic. The N distribution gave the best-fit result for 51% of the stations. N2 and N3 gave the best-fit for 20% and 14% of stations, respectively. N5 gave 11% of the best-fit results. This study also calculated the rainfall heights corresponding to 10-year, 25-year, 50-year, and 100-year return periods for each location by using the distributions to project more extreme values.
Highlights
For analyzing the risk of rare events, extreme value analysis (EVA) is widely used in various disciplines, including environmental science [1], engineering [2], finance [3], and water resources engineering and management [4,5,6]
“return period”, the average recurrence interval between events. It can be derived from quantiles of a parametric probability distribution fitted to the extreme values [8]
The main goal of this paper is to identify the best-fit Gaussian mixture distribution model for every station which yields the maximum monthly rainfall for return periods of
Summary
For analyzing the risk of rare events, extreme value analysis (EVA) is widely used in various disciplines, including environmental science [1], engineering [2], finance [3], and water resources engineering and management [4,5,6]. The purpose of extreme event analysis, such as of floods or precipitation, is to estimate the risk to human beings and environments by extrapolating the observed range of sample data. The extreme events are expressed in terms of recurrence interval or “return period”, the average recurrence interval between events. It can be derived from quantiles of a parametric probability distribution fitted to the extreme values [8]
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