A New Probability Model for Hydrologic Events: Properties and Applications

Abstract

Upon the motivation of unstable climatic conditions of the world like excess of rains, drought and huge floods, we introduce a versatile hydrologic probability model with two scale parameters. The proposed model contains Lindley and exponentiated exponential (Lindley in J R Stat Soc Ser B 20:102–107, 1958; Gupta and Kundu in Biom J 43(1):117–130, 2001) distributions as special cases. Various properties of the distribution are obtained, such as shapes of the density and hazard functions, moments, mean deviation, information-generating function, conditional moments, Shannon entropy, L-moments, order statistics, information matrix and characterization via hazard function. Parameters are estimated via maximum likelihood estimation method. A simulation scheme is provided for generating the random data from the proposed distribution. Four data sets are used for comparing the proposed model with a set of well-known hydrologic models, such as generalized Pareto, log normal (3), log Pearson type III, Kappa(3), Gumbel, generalized logistic and generalized Lindley distributions, using some goodness-of-fit tests. These comparisons render the proposed model suitable and representative for hydrologic data sets with least loss of information attitude and a realistic return period, which render it as an appropriate alternate of the existing hydrologic models. Supplementary materials for this paper are available online.