A Flexible Extension of Pareto Distribution: Properties and Applications.

Huda M Alshanbari,Ahmed Sedky Eldeeb,Ahmed M Gemeay,Abd Al-Aziz Hosni El-Bagoury,E H Hafez,Ahmed Mostafa Khalil

doi:10.1155/2021/9819200

Abstract

This paper introduced a relatively new mixture distribution that results from a mixture of Fréchet–Weibull and Pareto distributions. Some properties of the new statistical model were derived, such as moments with their related measures, moment generating function, mean residual life function, and mean deviation. Furthermore , different estimation methods were introduced for determining the unknown parameters of the proposed model. Finally, we introduced three real data sets which were applied to our distribution and compared them with other well-known statistical competitive models to show the superiority of our model for fitting the three real data sets, and we can clearly see that our distribution outperforms its competitors. Also, to verify our results, we carried out the existence and uniqueness test to the log-likelihood to determine whether the roots are global maximum or not.

Highlights

Modeling new phenomena is very important in the field of big data and data science. ere are many ways for modeling and representing data
We introduced a new mixture of distribution Frechet–Weibull mixture Pareto distribution (FWMPD), and we estimated its parameters by the classical methods of estimation: the maximum likelihood estimation and 7 other methods
We introduced its mathematical properties and graphed its probability density function (PDF) and cumulative distribution function (CDF) to study its behavior under different values of estimates

Summary

Introduction

Modeling new phenomena is very important in the field of big data and data science. ere are many ways for modeling and representing data. 2. The Mixture of Frechet–Weibull and Pareto Distributions e formulation of the new mixture model is presented in this part of the paper . If a random variable X follows Frechet–Weibull distribution and by taking one of its four parameters (λ) as a random variable following Pareto distribution, it is said to have FWMPD when its PDF and CDF are, respectively, defined as follows: f(x) abaβa/kx− a− 1Γ⎡⎣1 −. Is section contains studies on the behaviors of PDF, CDF, and S(x) of FWMPD at x 0 and x ∞, respectively, as follows: lim f(x) abaβa/k lim x− a− 1 lim Γ⎡⎣1 −.

Statistical Properties

Conclusion and Major Findings