Haitham M. Yousof

In this paper, we introduce a new class of distributions called the Burr X family. Some of its mathematical and structural properties are derived. The maximum likelihood is used for estimating the model parameters. The importance and flexibility of the new family are illustrated by means of an application to real data set.

The Fréchet distribution is an absolutely continuous distribution with wide applicability in extreme value theory. Generalizing distributions is always precious for applied statisticians and recent literature has suggested several ways of extending well-known distributions. We propose a new lifetime model called the Kumaraswamy Marshall–Olkin Fréchet distribution, which generalizes the Marshall–Olkin Fréchet distribution and at least seventeen known and unknown lifetime models. Various properties of the new model are explored including closed-forms expressions for moments, quantiles, generating function, order statisics and Rényi entropy. The maximum likelihood method is used to estimate the model parameters. We compare the flexibility of the proposed model with other related distributions by means of two real data sets.

This paper introduces a new four-parameter lifetime model called the Weibull Burr XII distribution. The new model has the advantage of being capable of modeling various shapes of aging and failure criteria. We derive some of its structural properties including ordinary and incomplete moments, quantile and generating functions, probability weighted moments and order statistics. The new density function can be expressed as a linear mixture of Burr XII densities. We propose a log-linear regression model using a new distribution so-called the log-Weibull Burr XII distribution. The maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimation are discussed. We prove empirically the importance and flexibility of the new model in modeling various types of data.

We introduce a new family of continuous distributions called the complementary geometric transmuted-G family, which extends the trans-muted family proposed by Shaw and Buckley (2007). Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, quantile and generating functions, entropies, order statistics and probability weighted moments are derived. Two special models of the introduced family are discussed in detail. The maximum likelihood method is used for estimating the model parameters. The importance and flexibility of the new family are illustrated by means of two applications to real data sets. We provide some simulation results to assess the performance of the proposed model.

A new class of continuous distributions called the exponen-tiated Weibull-H family is proposed and studied. The proposed class extends the Weibull-H family of probability distributions introduced by Bourguignon et al. (J Data Sci 12:53–68, 2014). Some special models of the new family are presented. Its basic mathematical properties including explicit expressions for the ordinary and incomplete moments, quan-tile and generating function, Rényi and Shannon entropies, order statistics , and probability weighted moments are derived. The maximum-likelihood method is adopted to estimate the model parameters and a simulation study is performed. The flexibility of the generated family is proved empirically by means of two applications to real data sets.

We introduce a new class of continuous distributions called the transmuted exponentiated generalized-G family which extends the exponentiated generalized-G class introduced by Cordeiro et al. (2013). We provide some special models for the new family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Rényi and Shannon entropies, order statistics and probability weighted moments are derived. The estimation of the model parameters is performed by maximum likelihood. The flexibility of the proposed family is illustrated by means of an application to a real dataset.

A new five parameter model is proposed and stutied. The new distribution generalizes the Weibull Lomax distribution introduced by Tahir et al. (2015) and is referred to as transmuted Weibull Lomax (TWL) distribution. Various structural properties of the new model including ordinary and incomplete moments, quantiles, generating function, probability weighted moments, Rényi and q-entropies and order statistics are derived. We proposed the method of maximum likelihood for estimating the model parameters. The usefulness of the new model is illustrated through an application to a real data set.

We  introduce  a  new  family  of  continuous  distributions  called  the  transmuted geometric-G  family  which  extends  the  transmuted  family  pioneered  by  Shaw  and Buckley (2007). Some  of its  mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Rényi and Shannon entropies,
order statistics and probability  weighted  moments are  derived.  Some  special  models of the new family are provided. The maximum likelihood method is used for estimating the
model parameters. The importance and flexibility of the proposed family are illustrated by two applications to real data sets.

A new generalization of the Weibull-Pareto distribution called the transmuted Weibull-Pareto distribution is proposed and studied. Various mathematical properties of this distribution including ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves and order statistics are derived. The method of maximum likelihood is used for estimating the model parameters. The flexibility of
the new lifetime model is illustrated by means of an application to a real data set.

A new generalization of the Weibull-Pareto distribution called the exponentiated Weibull-Pareto distribution is defined and studied. Various structural properties including ordinary moments, quantiles, Renyi and q-entropies and order statistics are derived. We proposed the method of maximum likelihood for estimating the model parameters. We provide the simulation results to assess the performance of the proposed model. The usefulness and flexibility of the new model is illustrated using real data.

A new four-parameter lifetime model called the Weibull Fréchet distribution is defined and studied. Various of its structural properties including ordinary and incomplete moments, quantile and generating functions, probability weighted moments, Rényi and δ-entropies and order statistics are investigated. The new density function can be expressed as a linear mixture of Fréchet densities. The maximum likelihood method is used to estimate the model parameters. The new distribution is applied to two real data sets to prove empirically its flexibility. It can serve as an alternative model to other lifetime distributions in the existing literature for modeling positive real data in many areas.

We introduce a new class of continuous distributions called the transmuted exponentiated generalized-G family which extends the exponentiated generalized-G class introduced by Cordeiro et al. (2013). We provide some special models for the new family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Rényi and Shannon entropies, order statistics and probability weighted moments are derived. The estimation of the model parameters is performed by maximum likelihood. The flexibility of the proposed family is illustrated by means of an application to a real dataset.

This paper introduces a new generalization of the transmuted Marshall-Olkin Fréchet distribution of Afify et al. (2015), using Kumaraswamy generalized family. The new model is referred to as Kumaraswamy transmuted Marshall-Olkin Fréchet distribution. This model contains sixty two sub-models as special cases such as the Kumaraswamy transmuted Fréchet, Kumaraswamy transmuted Marshall-Olkin, generalized inverse Weibull and Kumaraswamy Gumbel type II distributions, among others. Various mathematical properties of the proposed distribution including closed forms for ordinary and incomplete moments, quantile and generating functions and Rényi and-entropies are derived. The unknown parameters of the new distribution are estimated using the maximum likelihood estimation. We illustrate the importance of the new model by means of two applications to real data sets.

We propose and study a new class of continuous distributions called the beta Weibull-G family which extends the Weibull-G family introduced by Bourguignon et al. (2014). Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, order statistics and probability weighted moments are derived. The maximum likelihood is used for estimating the model parameters. The importance and flexibility of the new family are illustrated by means of two applications to real data sets.