Ahmed Z. Afify

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 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.

A new extension of weibull distribution: Properties and different methods of estimation

Abstract The Weibull distribution has been generalized by many authors in recent years. Here, we introduce a new generalization of the Weibull distribution, called Alpha logarithmic transformed Weibull distribution that provides better fits than some of its known generalizations. The proposed distribution contains Weibull, exponential, logarithmic transformed exponential and logarithmic transformed Weibull distributions as special cases. Our main focus is the estimation from frequentist point of view of the unknown parameters along with some mathematical properties of the new model. The proposed distribution accommodates monotonically increasing, decreasing, bathtub and unimodal and then bathtub shape hazard rates, so it turns out to be quite flexible for analyzing non-negative real life data. We briefly describe different frequentist approaches, namely, maximum likelihood estimators, percentile based estimators, least squares estimators, weighted least squares estimators, maximum product of spacings estimators and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. The potentiality of the distribution is analyzed by means of two real data sets.

The odd Lomax generator of distributions: Properties, estimation and applications

Abstract We introduce a new family of continuous distributions called the odd Lomax-G class and provide four special models. We derive explicit expressions for the ordinary and incomplete moments, generating function, Renyi entropy, order statistics and probability weighted moments. The maximum likelihood and least squares methods are used to estimate the model parameters. The flexibility of the proposed family is illustrated by means of two applications to real data sets.

The Weibull Marshall–Olkin family: Regression model and application to censored data

Abstract We introduce a new class of distributions called the Weibull Marshall–Olkin-G family. We obtain some of its mathematical properties. The special models of this family provide bathtub-shaped, decreasing-increasing, increasing-decreasing-increasing, decreasing-increasing-decreasing, monotone, unimodal and bimodal hazard functions. The maximum likelihood method is adopted for estimating the model parameters. We assess the performance of the maximum likelihood estimators by means of two simulation studies. We also propose a new family of linear regression models for censored and uncensored data. The flexibility and importance of the proposed models are illustrated by means of three real data sets.

A new aging concept derived from the increasing convex ordering

Abstract In this paper, a comparison between the life distribution of a new unit with that of a used unit in the increasing convex order is made leading to a new class of life distributions which we call “new better than used in convex ordering of second order”. This class includes as subclasses the NBU and the NBUC and is a subclass of the NBUCA class. Preservation properties under convolution, random maxima, mixing and formation of coherent structures are established. Stochastic comparisons of the excess lifetime when the inter-arrival times belong to the NBUC(2) class are developed. Some applications of Poisson shock models and a test of exponentiality against NBUC(2) alternative are presented.

Toward the evaluation of P(X(t) > Y(t)) when both X(t) and Y(t) are inactivity times of two systems

ABSTRACT The inactivity time, also known as reversed residual life, has been a topic of increasing interest in the literature. In this investigation, based on the comparison of inactivity times of two devices, we introduce and study a new estimate of the probability of the inactivity time of one device exceeding that of another device. The problem studied in this paper is important for engineers and system designers. It would enable them to compare the inactivity times of the products and, hence to design better products. Several properties of this probability are established. Connections between the target probability and the reversed hazard rates of the two devices are established. In addition, some of the reliability properties of the new concept are investigated extending the well-known probability ordering. Finally, to illustrate the introduced concepts, many examples and applications in the context of reliability theory are included.