A novel extension of Fréchet distribution: Application on real data and simulation

Abstract

In this manuscript we introduce a new distribution called the novel alpha power Fréchet(NAPF) distribution. We introduce its mathematical properties and its probability density function (PDF) and Cumulative distribution function (CDF) in a closed form. We made a simulation study to estimate the parameters of the proposed distribution. We made point estimation using six classical methods. We generated complete sample using the R software that used in the estimation process. We applied different real data sets on the proposed distribution to asses the performance of it against all its competitors. We used different type of data. We used the Kolimingrov Sminrov (KS) algorithm to make the goodness of fit test for the complete data. We estimated all information criteria and we deduced that the proposed distribution outperforms all its competitors, and we concluded that the proposed distribution is a very good candidate for modelling complete data. We studied the existence and uniqueness of the log-likelihood function which must be studied to make sure that the likelihood function provides maximum estimates for the parameters.

Keywords

• Fréchet Distribution
• Moments
• Entropy
• Estimation methods