Haitham M. Yousof

The generalized transmuted-G family of distributions

ABSTRACT We introduce a new class of continuous distributions called the generalized transmuted-G family which extends the transmuted-G class. We provide six special models of 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 three applications to real data sets.

The Weibull Fréchet distribution and its applications

ABSTRACT 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 -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.

The Burr X Generator of Distributions for Lifetime Data

The statistical literature contains many new classes of distributions which have been constructed by extending common families of continuous distributions by means of adding one or more shape parameters. The inducted extra parameter(s) to the existing probability distribution have been shown to improve the flexibility and goodness of fits of the distribution against the intuition of model parsimony. Therefore, many methods of adding a parameter to distributions have been proposed by several researchers and these new families have been used for modeling data in many applied areas such as engineering, economics, biological studies, environmental sciences and many more. In fact the modern computing technology has made many of these techniques accessible if the analytical solutions are very complicated. Gupta et al. [18] defined the exponentiated-G (exp-G) class, which consists of raising the cumulative distribution function (cdf) to a positive power parameter and proposed the exponentiated exponential (EE) distribution, defined by the cdf (for x > 0) F(x) = [1− exp(−λx)]θ , where λ ,θ > 0. This equation is simply the θ th power of the standard exponential cumulative distribution. Many Journal of Statistical Theory and Applications, Vol. 16, No. 3 (September 2017) 288–305 ___________________________________________________________________________________________________________

The exponentiated transmuted-G family of distributions: Theory and applications

ABSTRACT In this paper, a new family of continuous distributions called the exponentiated transmuted-G family is proposed which extends the transmuted-G family defined 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, and order statistics are derived. Some special models of the new family are provided. The maximum likelihood is used 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 family is illustrated using real data.

The ExponentiatedWeibull-Pareto Distribution with Application

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, Rényi 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.

The Four-Parameter Burr XII Distribution: Properties, Regression Model and Applications

ABSTRACT 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.

The Exponentiated Generalized-G Poisson Family of Distributions

In this article we propose and study a new family of distributions which is defined by using the genesis of the truncated Poisson distribution and the exponentiated generalized-G distribution. Somemathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics and their moments, reliability and Shannon entropy are derived. Estimation of the parameters using the method of maximum likelihood is discussed. Although this generalization technique can be used to generalize many other distributions, in this study we present only two special models. The importance and flexibility of the new family is exemplified using real world data.

The Transmuted Weibull-G Family of Distributions

We introduce a new family of continuous distributions called the transmuted Weibull-G family of distributions which extends the transmuted class pioneered by Shaw and Buckley (2007). We study the mathematical properties of the new family. Some useful characterizations based on the ratio of two truncated moments as well as based on hazard function are presented. We estimate the model parameters by the maximum likelihood method. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of a simulation study.

A new family of distributions with properties, regression models and applications

Abstract In this study, we introduce a new family of continuous distributions with one extra shape parameter, called the Burr-Hatke-G family, based on the Burr-Hatke differential equation. Some of its mathematical properties are derived. The maximum likelihood method is used to estimate the model parameters. Moreover, the log-Burr-Hatke-Weibull regression model based on new the generated family is introduced. The usefulness of the proposed family is demonstrated by means of the three real data applications. Empirical results indicate that the proposed family provides more realistic fits than other well-known family of distributions.

Type I General Exponential Class of distributions

We introduce a new family of continuous distributions and study the mathematical properties of the new family. Some useful characterizations based on the ratio of two truncated moments and hazard function are also presented. We estimate the model parameters by the maximum likelihood method and assess its performance based on biases and mean squared errors in a simulation study framework.