This paper presents a novel two-parameter G family of distributions. Relevant statistical properties such as the ordinary moments, incomplete moments and moment generating function are derived. Using common copulas, some new bivariate type G families are derived. Special attention is devoted to the standard exponential base line model. The density of the new exponential extension can be “asymmetric and right skewed shape” with no peak, “asymmetric right skewed shape” with one peak, “symmetric shape” and “asymmetric left skewed shape” with one peak. The hazard rate of the new exponential distribution can be “increasing”, “U-shape”, “decreasing” and “J-shape”. The usefulness and flexibility of the new family is illustrated by means of two applications to real data sets. The new family is compared with many common G families in modeling relief times and survival times data sets.

In this work, we propose and study a new family of discrete distributions. Many useful mathematical properties, such as ordinary moments, moment generating function, cumulant generating function, probability generating function, central moment, and dispersion index are derived. Some special discrete versions are presented. A certain special case is discussed graphically and numerically. The hazard rate function of the new class can be “decreasing”, “upside down”, “increasing”, and “decreasing-constant-increasing (U-shape)”. Some useful characterization results based on the conditional expectation of certain function of the random variable and in terms of the hazard function are derived and presented. Bayesian and non-Bayesian methods of estimation are considered. The Bayesian estimation procedure under the squared error loss function is discussed. Markov chain Monte Carlo simulation studies for comparing non-Bayesian and Bayesian estimations are performed using the Gibbs sampler and Metropolis–Hastings algorithm. Four applications to real data sets are employed for comparing the Bayesian and non-Bayesian methods. The importance and flexibility of the new discrete class is illustrated by means of four real data applications.

In this article, we introduce a new generalization of the Exponentiated Exponential distribution. Various structural mathematical properties are derived. Numerical analysis for mean, variance, skewness and kurtosis and the dispersion index are performed. The new density can be right skewed and symmetric with "unimodal" and "bimodal" shapes. The new hazard function can be "constant", "monotonically decreasing", "monotonically increasing", "increasing-constant", "upside-down-constant", "decreasing-constant". Many bivariate and multivariate type model have been also derived. We assess the performance of the maximum likelihood method graphically via the biases and mean squared errors. The applicability of the new life distribution is illustrated by means of two real data sets.

A new compound Lomax model is proposed and analyzed. The novel distribution is derived based on compounding the zero truncated Poisson distribution and the exponentiated exponential Lomax distribution. The new density can be “monotonically left skewed,” “monotonically right skewed” and “symmetric” with various useful shapes. The new hazard rate can be “upside down bathtub-increasing,” “bathtub (U-shape),” “monotonically decreasing,” “increasing-constant” and “monotonically increasing.” Relevant statistical properties are derived. We briefly describe different estimation methods, namely the maximum likelihood, Cramér-von-Mises, ordinary least squares, weighted least square, Anderson–Darling, right tail Anderson–Darling and left tail Anderson–Darling. Monte Carlo simulation experiments are performed for comparing the performances of the proposed methods of estimation for both small and large samples. For facilitating the mathematical modeling of the bivariate real data sets, we derive some new corresponding bivariate distributions. Graphical simulation study is performed for assessing the finite sample behavior of the estimators using the maximum likelihood method. Two applications are provided for illustrating the applicability of the new model.

In this work, we introduced a new three-parameter Nadarajah-Haghighi model. We derived explicit expressions for some of its statistical properties. The Farlie Gumbel Morgenstern, modified Farlie Gumbel Morgenstern, Clayton, Renyi and Ali-Mikhail-Haq copulas are used for deriving some bivariate type extensions. We consider maximum likelihood, Cramer-vonMises, ordinary least squares, weighted least squares, Anderson Darling, right tail Anderson Darling and left tail Anderson Darling estimation procedures to estimate the unknown model parameters. Simulation study for comparing estimation methods is performed. An application for comparing methods as also presented. The maximum likelihood estimation method is the best method. However, the other methods performed well. Another application for comparing the competitive models is investigated.

A new lifetime model is introduced and studied. The major justi…cation for the practicality of the new model is based on the wider use of the Lomax model. We are also motivated to introduce the new model since the density of the new distribution exhibits various important shapes such as the unimodal, right skewed and left skewed. The new model can be viewed as a mixture of the exponentiated Lomax distribution. It can also be considered as a suitablemodel for testing the symmetric, left skewed, right skewed and unimodal data. The maximum likelihood estimation method is used to estimate the model parameters. We prove empirically the importance and ‡exibility of the new model in modeling two types of aircraft windshield lifetime data sets. The proposed lifetime model is much better than gamma Lomax, beta Lomax, exponentiated Lomax and Lomax models so the exponentiated Lomax, model is a good alternative to these models in modeling aircraft windshield data.