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Abstract

Modeling of some rarely occurring environmental events, obtaining and analyzing accurate predictions is quite important in determining the nature of such events and taking measures accordingly. Modeling these rarely occurring environmental events with the statistical distributions in the literature may cause some problems. For this reason, different statistical distributions are needed for modeling this type of rare data. In this paper, a new three-parameter exponentiated Benini distribution based on the exponential family is proposed as a new lifetime distribution. It is called the three-parameter exponentiated Benini distribution. Although new distributions are derived by different methods in the literature, there is no study on three-parameter Benini distribution. In this study, we firstly examine to different mathematical properties and performance in real life applications of exponential Benini distribution. Some of its fundamental structural properties are described, such as the survival function, hazard function, quantile function, skewness and kurtosis coefficients. Also, results on stochastic ordering, moments, incomplete moments and ordered statistics are obtained. Then, the parameters of the proposed distribution are estimated by using the maximum likelihood method. Applying the proposed distribution on two real environmental data, it is obtained that the exponentiated Benini distribution is favorable over the Benini, Ramous Louzada, inverse Pareto, Pareto, Pareto Type I, Pareto Type II, Beta Paretoand Weibull Preto, showing the best fitting results. As a result, we have found that the proposed distribution in modeling environmental data gives more unbiased and best fitting results than other distributions.

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