New Three-Parameter Exponentiated Benini Distribution: Properties and Applications

Modelling some rare environmental events and obtaining accurate predictions is quite important to determine their nature and to take action accordingly. In this article, a new three-parameter exponentiated Benini distribution based on the exponential family is proposed for this purpose. It is called the three-parameter exponentiated Benini distribution. As an additional motivation, although new distributions are derived by various methods in the literature, there is no study on variants of the Benini distribution. We first investigate its mathematical properties and then evaluate its performance in real applications by comparing it with other distributions. In particular, the corresponding probability density and hazard rate functions, quantile function, stochastic ordering, moment and incomplete moment, and ordered statistics, are presented in detail. The analysis of the shape of the distribution is also provided by calculating the skewness and kurtosis coefficients for different parameter values. In addition, several classical estimates for the parameters of the three-parameter exponential Benini distribution are computed, including maximum likelihood estimates, maximum product of distance estimates, Anderson-Darling estimates, right and left tail Anderson-Darling estimates, and Cramér-von Mises estimates. We examine the performance of these methods with simulation studies via different scenarios and sample sizes. Applying the proposed distribution to two real environmental data sets, we find that the three-parameter exponential Benini distribution gives the best results compared to the Benini, Ramous Louzada, inverse Pareto, Pareto, Pareto type I, Pareto type II, Beta Pareto and Weibull Pareto distributions. Overall, it is particularly adapted to the analysis of environmental data, mainly due to its long-tailed and flexible structure.