The gamma-Lomax distribution

For any continuous baseline G distribution, Zografos and Balakrishnan [On families of beta- and generalized gamma-generated distributions and associated inference. Statist Methodol. 2009;6:344–362] proposed a generalized gamma-generated distribution with an extra positive parameter. A new three-parameter continuous distribution called the gamma-Lomax distribution, which extends the Lomax distribution is proposed and studied. Various structural properties of the new distribution are derived including explicit expressions for the moments, generating and quantile functions, mean deviations and Rényi entropy. The estimation of the model parameters is performed by maximum likelihood. We also determine the observed information matrix. An application illustrates the usefulness of the proposed model.     

The Poisson Generalized Linear Failure Rate Model

We formulate a new cure rate survival model by assuming that the number of competing causes of the event of interest has the Poisson distribution, and the time to this event has the generalized linear failure rate distribution. A new distribution to analyze lifetime data is defined from the proposed cure rate model, and its quantile function as well as a general expansion for the moments is derived. We estimate the parameters of the model with cure rate in the presence of covariates for censored observations using maximum likelihood and derive the observed information matrix. We obtain the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and present some ways to perform global influence analysis. The usefulness of the proposed cure rate survival model is illustrated in an application to real data.     

A new generalization of the Weibull-geometric distribution with bathtub failure rate

In this paper, the researchers attempt to introduce a new generalization of the Weibull-geometric distribution. The failure rate function of the new model is found to be increasing, decreasing, upside-down bathtub, and bathtub-shaped. The researchers obtained the new model by compounding Weibull distribution and discrete generalized exponential distribution of a second type, which is a generalization of the geometric distribution. The new introduced model contains some previously known lifetime distributions as well as a new one. Some basic distributional properties and moments of the new model are discussed. Estimation of the parameters is illustrated and the model with two known real data sets is examined.     

The exponential–Weibull lifetime distribution

In this paper, we propose a new three-parameter model called the exponential–Weibull distribution, which includes as special models some widely known lifetime distributions. Some mathematical properties of the proposed distribution are investigated. We derive four explicit expressions for the generalized ordinary moments and a general formula for the incomplete moments based on infinite sums of Meijer's G functions. We also obtain explicit expressions for the generating function and mean deviations. We estimate the model parameters by maximum likelihood and determine the observed information matrix. Some simulations are run to assess the performance of the maximum likelihood estimators. The flexibility of the new distribution is illustrated by means of an application to real data.     

The beta generalized exponential distribution

A new distribution called the beta generalized exponential distribution is proposed. It includes the beta exponential and generalized exponential (GE) distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. The density function can be expressed as a mixture of generalized exponential densities. This is important to obtain some mathematical properties of the new distribution in terms of the corresponding properties of the GE distribution. We derive the moment generating function (mgf) and the moments, thus generalizing some results in the literature. Expressions for the density, mgf and moments of the order statistics are also obtained. We discuss estimation of the parameters by maximum likelihood and obtain the information matrix that is easily numerically determined. We observe in one application to a real skewed data set that this model is quite flexible and can be used effectively in analyzing positive data in place of the beta exponential and GE distributions.     

The log-exponentiated generalized gamma regression model for censored data

For the first time, we introduce a generalized form of the exponentiated generalized gamma distribution [Cordeiro et al. The exponentiated generalized gamma distribution with application to lifetime data, J. Statist. Comput. Simul. 81 (2011), pp. 827–842.] that is the baseline for the log-exponentiated generalized gamma regression model. The new distribution can accommodate increasing, decreasing, bathtub- and unimodal-shaped hazard functions. A second advantage is that it includes classical distributions reported in the lifetime literature as special cases. We obtain explicit expressions for the moments of the baseline distribution of the new regression model. The proposed model can be applied to censored data since it includes as sub-models several widely known regression models. It therefore can be used more effectively in the analysis of survival data. We obtain maximum likelihood estimates for the model parameters by considering censored data. We show that our extended regression model is very useful by means of two applications to real data.     

Transmuted generalized exponential distribution: A generalization of the exponential distribution with applications to survival data

In this article, we investigate the potential usefulness of the three-parameter transmuted generalized exponential distribution for analyzing lifetime data. We compare it with various generalizations of the two-parameter exponential distribution using maximum likelihood estimation. Some mathematical properties of the new extended model including expressions for the quantile and moments are investigated. We propose a location-scale regression model, based on the log-transmuted generalized exponential distribution. Two applications with real data are given to illustrate the proposed family of lifetime distributions.     

Failure Rate and Aging Properties of Generalized Beta- and Gamma-generated Distributions

In the present article we study several characteristics of the families of generalized beta- and gamma- generated distributions introduced by Alexander et al. (2011) and Zografos and Balakrishnan (2009), respectively. Simple formulas are established for calculating the failure rate of the members of the aforementioned families by exploiting the failure rate of the parent distribution. In addition, the aging properties of the generalized beta- and gamma-generated distributions are explored in terms of the corresponding aging behavior of the parent family.     

The McDonald arcsine distribution: a new model to proportional data

We propose a new three-parameter continuous model called the McDonald arcsine distribution, which is a very competitive model to the beta, beta type I and Kumaraswamy distributions for modelling rates and proportions. We provide a mathematical treatment of the new distribution including explicit expressions for the density function, moments, generating and quantile functions, mean deviations, two probability measures based on the Bonferroni and Lorenz curves, Shannon entropy, Rényi entropy and cumulative residual entropy. Maximum likelihood is used to estimate the model parameters and the expected information matrix is determined. An application of the proposed model to real data shows that it can give consistently a better fit than other important statistical models.     

Modified slashed generalized exponential distribution

Abstract

In this article, we introduce a new distribution for modeling positive data sets with high kurtosis, the modified slashed generalized exponential distribution. The new model can be seen as a modified version of the slashed generalized exponential distribution. It arises as a quotient of two independent random variables, one being a generalized exponential distribution in the numerator and a power of the exponential distribution in the denominator. We studied various structural properties (such as the stochastic representation, density function, hazard rate function and moments) and discuss moment and maximum likelihood estimating approaches. Two real data sets are considered in which the utility of the new model in the analysis with high kurtosis is illustrated.     

A generalization of discrete Weibull distribution

In this paper, we introduce a new family of discrete distributions and study its properties. It is shown that the new family is a generalization of discrete Marshall-Olkin family of distributions. In particular, we study generalized discrete Weibull distribution in detail. Discrete Marshall-Olkin Weibull distribution, exponentiated discrete Weibull distribution, discrete Weibull distribution, discrete Marshall-Olkin generalized exponential distribution, exponentiated geometric distribution, generalized discrete exponential distribution, discrete Marshall-Olkin Rayleigh distribution and exponentiated discrete Rayleigh distribution are sub-models of generalized discrete Weibull distribution. We derive some basic distributional properties such as probability generating function, moments, hazard rate and quantiles of the generalized discrete Weibull distribution. We can see that the hazard rate function can be decreasing, increasing, bathtub and upside-down bathtub shape. Estimation of the parameters are done using maximum likelihood method. A real data set is analyzed to illustrate the suitability of the proposed model.     

A new family of generalized distributions

Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 462 (1980), pp. 79–88] introduced a distribution for double-bounded random processes with hydrological applications. For the first time, based on this distribution, we describe a new family of generalized distributions (denoted with the prefix ‘Kw’) to extend the normal, Weibull, gamma, Gumbel, inverse Gaussian distributions, among several well-known distributions. Some special distributions in the new family such as the Kw-normal, Kw-Weibull, Kw-gamma, Kw-Gumbel and Kw-inverse Gaussian distribution are discussed. We express the ordinary moments of any Kw generalized distribution as linear functions of probability weighted moments (PWMs) of the parent distribution. We also obtain the ordinary moments of order statistics as functions of PWMs of the baseline distribution. We use the method of maximum likelihood to fit the distributions in the new class and illustrate the potentiality of the new model with an application to real data.     

An extended Lomax distribution

A new five-parameter continuous distribution, the so-called McDonald Lomax distribution, that extends the Lomax distribution and some other distributions is proposed and studied. The model has as special sub-models new four- and three-parameter distributions. Various structural properties of the new distribution are derived, including expansions for the density function, explicit expressions for the moments, generating and quantile functions, mean deviations and Rényi entropy. The score function is derived and the estimation is performed by maximum likelihood. We also obtain the observed information matrix. An application illustrates the usefulness of the proposed model.     

A new weighted distribution as an extension of the generalized half-normal distribution with applications

In this study, a new extension of generalized half-normal (GHN) distribution is introduced. Since this new distribution can be viewed as weighted version of GHN distribution, it is called as weighted generalized half-normal (WGHN) distribution. It is shown that WGHN distribution can be observed as a single constrained and hidden truncation model. Therefore, the new distribution is more flexible than the GHN distribution. Some statistical properties of the WGHN distribution are studied, i.e. moments, cumulative distribution function, hazard rate function are derived. Furthermore, maximum likelihood estimation of the parameters is considered. Some real-life data sets taken from the literature are modelled using the WGHN distribution. It is seen that for these data sets the WGHN distribution provides better fitting than the GHN and slashed generalized half-normal (SGHN) distributions.     

A new discrete probability distribution with integer support on (−∞, ∞)

ABSTRACT

A new discrete probability distribution with integer support on (?∞, ∞) is proposed as a discrete analog of the continuous logistic distribution. Some of its important distributional and reliability properties are established. Its relationship with some known distributions is discussed. Parameter estimation by maximum-likelihood method is presented. Simulation is done to investigate properties of maximum-likelihood estimators. Real life application of the proposed distribution as empirical model is considered by conducting a comparative data fitting with Skellam distribution, Kemp's discrete normal, Roy's discrete normal, and discrete Laplace distribution.     

General results for the beta-modified Weibull distribution

We study in detail the so-called beta-modified Weibull distribution, motivated by the wide use of the Weibull distribution in practice, and also for the fact that the generalization provides a continuous crossover towards cases with different shapes. The new distribution is important since it contains as special sub-models some widely-known distributions, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among several others. It also provides more flexibility to analyse complex real data. Various mathematical properties of this distribution are derived, including its moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are also derived for the chf, mean deviations, Bonferroni and Lorenz curves, reliability and entropies. The estimation of parameters is approached by two methods: moments and maximum likelihood. We compare by simulation the performances of the estimates from these methods. We obtain the expected information matrix. Two applications are presented to illustrate the proposed distribution.     

General properties for the beta extended half-normal model

We formulate and study a four-parameter lifetime model called the beta extended half-normal distribution. This model includes as sub-models the exponential, extended half-normal and half-normal distributions. We derive expansions for the new density function which do not depend on complicated functions. We obtain explicit expressions for the moments and incomplete moments, generating function, mean deviations, Bonferroni and Lorenz curves and Rényi entropy. In addition, the model parameters are estimated by maximum likelihood. We provide the observed information matrix. The new model is modified to cope with possible long-term survivors in the data. The usefulness of the new distribution is shown by means of two real data sets.     

The Marshall–Olkin extended generalized Lindley distribution: Properties and applications

In this article, we define and study a new three-parameter model called the Marshall–Olkin extended generalized Lindley distribution. We derive various structural properties of the proposed model including expansions for the density function, ordinary moments, moment generating function, quantile function, mean deviations, Bonferroni and Lorenz curves, order statistics and their moments, Rényi entropy and reliability. We estimate the model parameters using the maximum likelihood technique of estimation. We assess the performance of the maximum likelihood estimators in a simulation study. Finally, by means of two real datasets, we illustrate the usefulness of the new model.     

The generalized transmuted-G family of distributions

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.     

A complementary generalized linear failure rate-geometric distribution

In this article, we shall attempt to introduce a new class of lifetime distributions, which enfolds several known distributions such as the generalized linear failure rate distribution and covers both positive as well as negative skewed data. This new four-parameter distribution allows for flexible hazard rate behavior. Indeed, the hazard rate function here can be increasing, decreasing, bathtub-shaped, or upside-down bathtub-shaped. We shall first study some basic distributional properties of the new model such as the cumulative distribution function, the density of the order statistics, their moments, and Rényi entropy. Estimation of the stress-strength parameter as an important reliability property is also studied. The maximum likelihood estimation procedure for complete and censored data and Bayesian method are used for estimating the parameters involved. Finally, application of the new model to three real datasets is illustrated to show the flexibility and potential of the new model compared to rival models.