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A new probability model with application to heavy-tailed hydrological data

Hussain, Tassaddaq, Bakouch, Hassan S., Chesneau, Christophe
Environmental and ecological statistics 2019 v.26 no.2 pp. 127-151
Weibull statistics, climatic factors, data collection, drought, floods, hydrologic data, hydrologic models, probability, rain
Because of the dramatic changes that are being observed in the climatic conditions of the world, such as excess of rains, drought and huge floods, we introduce a versatile hydrologic probability model with three parameters. The proposed model is a combination of the Lomax and generalized Weibull distributions based on an exponent odd function. Main properties of the distribution are obtained, such as shapes of the probability density and hazard rate functions, quantile function, asymptotic distribution, information matrix and characterization via hazard rate function. Parameters are estimated via the maximum likelihood estimation method. Four data sets are used to compare the proposed model with a number of well-known hydrologic models. The proposed model is found to be suitable and representative for heavy-tailed hydrological data sets, with least loss of information attitude and a realistic return period.