Exponential Power Series Distribution Research Articles

Generalized extended Weibull power series family of distributions

In this study, we introduce a new family of models for lifetime data called generalized extended Weibull power series family of distributions by compounding generalized extended Weibull distributions and power series distributions. The compounding procedure follows the same setup carried out by Adamidis (1998). The proposed family contains all types of combinations between truncated discrete with generalized and non-generalized Weibull distributions. Some existing power series and subclasses of mixed lifetime distributions become special cases of the proposed family, such as the compound class of extended Weibull power series distributions proposed by Silva et al. (2013) and the generalized exponential power series distributions introduced by Mahmoudi and Jafari (2012). Some mathematical properties of the new class are studied, including the cumulative distribution function, density function, survival function, and hazard rate function. The method of maximum likelihood is used for obtaining a general setup for estimating the parameters of any distribution in this class. An expectation-maximization algorithm is introduced for estimating maximum likelihood estimates. Special subclasses and applications for some models in a real dataset are introduced to demonstrate the flexibility and the benefit of this new family.

The Power Series Exponential Power Series Distributions with Applications to Failure Data Sets

The Power Series Exponential Power Series Distributions with Applications to Failure Data Sets

On absolutely continuous bivariate generalized exponential power series distribution

Recently Mahmoudi and Jafari (2012) introduced generalized exponential power series distributions by compounding generalized exponential with the power series distributions. This is a very flexible distribution with some interesting physical interpretation. Kundu and Gupta (2011) introduced an absolute continuous bivariate generalized exponential distribution, whose marginals are generalized exponential distributions. The main aim of this paper is to introduce bivariate generalized exponential power series distributions. Two special cases namely bivariate generalized exponential geometric and bivariate generalized exponential Poisson distributions are discussed in details. It is observed that both the special cases are very flexible and their joint probability density functions can take variety of shapes. They have interesting copula structures and these can be used to study their different dependence structures and to compute different dependence measures. It is observed that both the models have six unknown parameters each, and the maximum likelihood estimators cannot be obtained in closed form. We have proposed to use EM algorithm to compute the maximum likelihood estimators of the unknown parameters. Some simulation experiments have been performed to see the effectiveness of the proposed EM algorithm. The analyses of two data sets have been performed for illustrative purposes, and it is observed that the proposed models and the EM algorithm work quite satisfactorily. Finally we provide the multivariate generalization of the proposed model.

A New Class of Beta-Complementary Exponential Power Series Distributions

Abstract In this paper, we introduce a new class of beta-complementary exponential power series distributions, which is obtained by replacing the cumulative distribution function of the complementary exponential power series distributions in the logit of a beta random variable. This new class of distributions contains some new submodels, such as beta-complementary exponential geometric, beta-complementary exponential Poisson, beta-complementary exponential binomial, beta-complementary exponential logarithmic, and complementary exponential power series distributions. A general class of distributions is presented and some various properties are obtained in this paper. We characterize the beta-complementary exponential geometric distribution as one of the most applicable distributions in this class. Some mathematical properties of the beta-complementary exponential geometric distribution are reached in terms of the corresponding properties of the complementary exponential geometric and beta exponential distributions. We present expressions for the probability density function, cumulative distribution function, moment generating function, and moments. The estimation of parameters is approached by the maximum likelihood estimation procedure, and the expected information matrix is derived. The flexibility of the distribution is illustrated in application of a real data set.

Classes of Univariate Continuous Exponential Power Series Distributions

Classes of Univariate Continuous Exponential Power Series Distributions

On some life distributions with flexible failure rate

A new three-parameter distribution family with a flexible failure rate function arising by mixing the Weibull distribution and power-series distribution is introduced. This distribution family includes special cases of some well-used mixing distributions and generalizes the exponential power-series distribution. Various properties of the new distribution family are discussed. The maximum likelihood estimation and an EM algorithm are presented for finding the estimates of the distribution family parameters, and expressions for their asymptotic variance and covariance are derived. Intensive simulation studies are implemented and experimental results are illustrated with real data-sets.

A new compounding family of distributions: The generalized gamma power series distributions

We propose a new four-parameter family of distributions by compounding the generalized gamma and power series distributions. The compounding procedure is based on the work by Marshall and Olkin (1997) and defines 76 sub-models. Further, it includes as special models the Weibull power series and exponential power series distributions. Some mathematical properties of the new family are studied including moments and generating function. Three special models are investigated in detail. Maximum likelihood estimation of the unknown parameters for complete sample is discussed. Two applications of the new models to real data are performed for illustrative purposes.

The complementary exponential power series distribution

In this paper, we introduce the complementary exponential power series distributions, with failure rate either increasing, which is complementary to the exponential power series model proposed by Chahkandi & Ganjali (2009). The new class of distribution arises on a latent complementary risks scenarios, where the lifetime associated with a particular risk is not observable, rather we observe only the maximum lifetime value among all risks. This new class contains several distributions as particular case. The properties of the proposed distribution class are discussed such as quantiles, moments and order statistics. Estimation is carried out via maximum likelihood. Simulation results on maximum likelihood estimation are presented. An real application illustrate the usefulness of the new distribution class.

Generalized exponential–power series distributions

In this paper, we introduce the generalized exponential–power series (GEPS) class of distributions, which is obtained by compounding generalized exponential and power series distributions. The compounding procedure follows the same way as previously carried out in introducing the complementary exponential–geometric (CEG) and the two-parameter Poisson–exponential (PE) lifetime distributions. This new class of distributions contains several lifetime models such as: CEG, PE, generalized exponential–binomial (GEB), generalized exponential–Poisson (GEP), generalized exponential–geometric (GEG) and generalized exponential–logarithmic (GEL) distributions as special cases.The hazard function of the GEPS distributions can be increasing, decreasing or bathtub shaped among others. We obtain several properties of the GEPS distributions such as moments, maximum likelihood estimation procedure via an EM-algorithm and inference for a large sample. Special distributions are studied in some detail. At the end, in order to show the flexibility and potentiality of the new class of distributions, we demonstrate applications of two real data sets.

A compound class of Weibull and power series distributions

In this paper we introduce the Weibull power series (WPS) class of distributions which is obtained by compounding Weibull and power series distributions, where the compounding procedure follows same way that was previously carried out by Adamidis and Loukas (1998). This new class of distributions has as a particular case the two-parameter exponential power series (EPS) class of distributions ( Chahkandi and Ganjali, 2009), which contains several lifetime models such as: exponential geometric ( Adamidis and Loukas, 1998), exponential Poisson ( Kus, 2007) and exponential logarithmic ( Tahmasbi and Rezaei, 2008) distributions. The hazard function of our class can be increasing, decreasing and upside down bathtub shaped, among others, while the hazard function of an EPS distribution is only decreasing. We obtain several properties of the WPS distributions such as moments, order statistics, estimation by maximum likelihood and inference for a large sample. Furthermore, the EM algorithm is also used to determine the maximum likelihood estimates of the parameters and we discuss maximum entropy characterizations under suitable constraints. Special distributions are studied in some detail. Applications to two real data sets are given to show the flexibility and potentiality of the new class of distributions.