An Extended Fr echet Distribution: Properties and Applications

Abstract

In this paper, we introduce an extended four-parameter Fr´echet model called the exponentiated exponential Fr´echet distribution, which arises from the quantile function of the standard exponential distribution. Various of its mathematical properties are derived including the quantile function, ordinary and incomplete moments, Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time, generating function, Shannon entropy and order statistics. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The usefulness of the new distribution is illustrated by means of three real lifetime data sets. In fact, the new model provides a better fit to these data than the Marshall-Olkin Fr´echet, exponentiated-Fr´echet and Fr´echet models.

The New Dagum-X Family of Distributions: Properties and Applications

“…For more illustration, this section compares the efficiency of the goodness-of-fit for the D-Fr distribution with some selected distributions in literature. In particular, two real data sets are used to compare the proposed model with four other distributions, namely, beta-Fréchet(BF) by [29], Gamma-Extended-Fréchet(GEF) by [30], Exponentiated-Exponential-Fréchet(EEF) by [31] and Fréchet(F) distributions by [32] which is also sudied by [33]. The first data set in Table (2) that is used in comparison is provided by Cordeiro and Silva [34].…”

Properties and Potentials of Gumbel Power Function Distribution to Rainfall and Wind Speed Datasets

“…Due to its tractability, power function has attracted the interest of many researchers who have attempted to extend it through the addition of shape parameters. Some extensions of power function distribution include Exponentiated Weibull-Power function Amal et al (2017), Exponentiated Weibull power function Hassan and Nassar (2017) Exponentaited Kumaraswamy-Power function Bursa and Ozel (2017), Kumaraswamy-Power Abdul-Moniem, (2017), Transmuted Power function Haq et al (2016), Log-Weighted Power function Mandouh and Mohamed (2020), Another generalized Transmuted Power function Nwezza and Uwadi (2021), Weibull-power function Tahir et al (2016), Transmuted Topp-Leone power function Hassan et al (2021), exponentiated generalized power function Hassan and Nassar (2020) and New cubic transmuted power function distribution Haq et al (2023). The transformed transformer (T-X) family of distribution was introduced by Alzaatreh et al (2013) as a method UWADI, U. U; NWEZZA, E. E; OKONKWO, C. I.…”

The New Mixed Generalized Erlang Distribution

“…These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. The basic definitions and properties of continuous random variables with their characteristics that are often used in order to introduce the Mixed distribution presents in [1] and [2]. A more general mixture is derived by Kadri and Halat [3], by proving the existence of such mixture by i w ∈  , and maintaining 1 given by Smaili et al [4], as:…”