The generalized odd log-logistic family of distributions: properties,regression models and applications

We propose a new class of continuous distributions with two extra shape parameters named the generalized odd log-logistic family of distributions. The proposed family contains as special cases the proportional reversed hazard rate and odd log-logistic classes. Its density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Some of its mathematical properties including ordinary moments, quantile and generating functions, two entropy measures and order statistics are obtained. We derive a power series for the quantile function. We discuss the method of maximum likelihood to estimate the model parameters. We study the behaviour of the estimators by means of Monte Carlo simulations. We introduce the log-odd log-logistic Weibull regression model with censored data based on the odd log-logistic-Weibull distribution. The importance of the new family is illustrated using three real data sets. These applications indicate that this family can provide better fits than other well-known classes of distributions. The beauty and importance of the proposed family lies in its ability to model different types of real data.     

The generalized odd half-Cauchy family of distributions: Properties and applications

We introduce and study general mathematical properties of a new generator of continuous distributions with one extra parameter called the generalized odd half-Cauchy family. We present some special models and investigate the asymptotics and shapes. The new density function can be expressed as a linear mixture of exponentiated densities based on the same baseline distribution. We derive a power series for the quantile function. We discuss the estimation of the model parameters by maximum likelihood and prove empirically the flexibility of the new family by means of two real data sets.     

The exponentiated G geometric family of distributions

We propose a new class of distributions called the exponentiated G geometric family motivated mainly by lifetime issues which can generate several lifetime models discussed in the literature. Some mathematical properties of the new family including asymptotes and shapes, moments, quantile and generating functions, extreme values and order statistics are fully investigated. We propose the log-exponentiated Weibull geometric and log-exponentiated log-logistic geometric regression models to cope with censored data. The model parameters are estimated by maximum likelihood. Three examples with real data expose quite well the new family.     

The odd power cauchy family of distributions: properties,regression models and applications

We study some mathematical properties of a new generator of continuous distributions with one extra parameter called the odd power Cauchy family including asymptotics, linear representation, moments, quantile and generating functions, entropies, order statistics and extreme values. We introduce two bivariate extensions of the new family. The maximum likelihood method is discussed to estimate the model parameters by means of a Monte Carlo simulation study. We define a new log-odd power Cauchy–Weibull regression model. The usefulness of the proposed models is proved empirically by means of three real data sets.     

The Topp–Leone odd log-logistic family of distributions

We introduce a new class of continuous distributions named the Topp–Leone odd log-logistic family, which extends the one-parameter distribution pioneered by Topp and Leone [A family of J-shaped frequency functions. J Amer Statist Assoc. 1955;50:209–219]. We study some of its mathematical properties and describe two special cases. Further, we propose a regression model based on the new Topp–Leone odd log-logistic Weibull distribution. The usefulness and flexibility of the proposed family are illustrated by means of three real data sets.     

The Kumaraswamy normal linear regression model with applications

ABSTRACT

For any continuous baseline G distribution, Cordeiro and Castro pioneered the Kumaraswamy-G family of distributions with two extra positive parameters, which generalizes both Lehmann types I and II classes. We study some mathematical properties of the Kumaraswamy-normal (KwN) distribution including ordinary and incomplete moments, mean deviations, quantile and generating functions, probability weighted moments, and two entropy measures. We propose a new linear regression model based on the KwN distribution, which extends the normal linear regression model. We obtain the maximum likelihood estimates of the model parameters and provide some diagnostic measures such as global influence, local influence, and residuals. We illustrate the potentiality of the introduced models by means of two applications to real datasets.     

The odd log-logistic Lindley Poisson model for lifetime data

We define two new lifetime models called the odd log-logistic Lindley (OLL-L) and odd log-logistic Lindley Poisson (OLL-LP) distributions with various hazard rate shapes such as increasing, decreasing, upside-down bathtub, and bathtub. Various structural properties are derived. Certain characterizations of OLL-L distribution are presented. The maximum likelihood estimators of the unknown parameters are obtained. We propose a flexible cure rate survival model by assuming that the number of competing causes of the event of interest has a Poisson distribution and the time to event has an OLL-L distribution. The applicability of the new models is illustrated by means real datasets.     

The type I half-logistic family of distributions

We study general mathematical properties of a new class of continuous distributions with an extra positive parameter called the type I half-logistic family. We present some special models and investigate the asymptotics and shapes. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. We derive a power series for the quantile function. Explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon and Rényi entropies and order statistics are determined. We introduce a bivariate extension of the new family. We discuss the estimation of the model parameters by maximum likelihood and illustrate its potentiality 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.     

A new compound class of log-logistic Weibull–Poisson distribution: model,properties and applications

A new class of distributions called the log-logistic Weibull–Poisson distribution is introduced and its properties are explored. This new distribution represents a more flexible model for lifetime data. Some statistical properties of the proposed distribution including the expansion of the density function, quantile function, hazard and reverse hazard functions, moments, conditional moments, moment generating function, skewness and kurtosis are presented. Mean deviations, Bonferroni and Lorenz curves, Rényi entropy and distribution of the order statistics are derived. Maximum likelihood estimation technique is used to estimate the model parameters. A simulation study is conducted to examine the bias, mean square error of the maximum likelihood estimators and width of the confidence interval for each parameter and finally applications of the model to real data sets are presented to illustrate the usefulness of the proposed distribution.     

The Exponentiated G Poisson Model

We study a new family of distributions defined by the minimum of the Poisson random number of independent identically distributed random variables having a general exponentiated G distribution. Some mathematical 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. Maximum likelihood estimation of the model parameters is investigated. Two special models of the new family are discussed. We perform an application to a real data set to show the potentiality of the proposed family.     

Cubic rank transmuted distributions: inferential issues and applications

In this paper, we introduce a new family of transmuted distributions, the cubic rank transmutation map distribution. This new proposal increases the flexibility of the transmuted distributions enabling the modelling of more complex data such as ones possessing bimodal hazard rates. In order to illustrate the usefulness of the cubic rank transmutation map, we use two well-known lifetime distributions, namely the Weibull and log-logistic models. Several mathematical properties of these new distributions, namely the cubic rank transmuted Weibull distribution and the cubic rank transmuted log-logistic distribution, are derived. Then, the maximum likelihood estimation of the model parameters is described. A simulation study designed to assess the properties of this estimation procedure is then carried out. Finally, applications of the proposed models and their fit are illustrated with some datasets and the corresponding diagnostic analyses are also provided.     

A new regression model for bimodal data and applications in agriculture

We define the odd log-logistic exponential Gaussian regression with two systematic components, which extends the heteroscedastic Gaussian regression and it is suitable for bimodal data quite common in the agriculture area. We estimate the parameters by the method of maximum likelihood. Some simulations indicate that the maximum-likelihood estimators are accurate. The model assumptions are checked through case deletion and quantile residuals. The usefulness of the new regression model is illustrated by means of three real data sets in different areas of agriculture, where the data present bimodality.     

The exponentiated-log-logistic geometric distribution: Dual activation

ABSTRACT

The log-logistic distribution is commonly used to model lifetime data. We propose a wider distribution, named the exponentiated log-logistic geometric distribution, based on a double activation approach. We obtain the quantile function, ordinary moments, and generating function. The method of maximum likelihood is used to estimate the model parameters. We propose a new extended regression model based on the logarithm of the exponentiated log-logistic geometric distribution. This regression model can be very useful in the analysis of real data and could provide better fits than other special regression models. The potentiality of the new models is illustrated by means of two applications to real lifetime data sets.     

Topp–Leone normal distribution with application to increasing failure rate data

In this article, we proposed a new three-parameter probability distribution, called Topp–Leone normal, for modelling increasing failure rate data. The distribution is obtained by using Topp–Leone-X family of distributions with normal as a baseline model. The basic properties including moments, quantile function, stochastic ordering and order statistics are derived here. The estimation of unknown parameters is approached by the method of maximum likelihood, least squares, weighted least squares and maximum product spacings. An extensive simulation study is carried out to compare the long-run performance of the estimators. Applicability of the distribution is illustrated by means of three real data analyses over existing distributions.     

The logistic-X family of distributions and its applications

ABSTRACT

The logistic distribution has a prominent role in the theory and practice of statistics. We introduce a new family of continuous distributions generated from a logistic random variable called the logistic-X family. Its density function can be symmetrical, left-skewed, right-skewed, and reversed-J shaped, and can have increasing, decreasing, bathtub, and upside-down bathtub hazard rates shaped. Further, it can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. We derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon entropy, and order statistics. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. We also investigate the properties of one special model, the logistic-Fréchet distribution, and illustrate its importance by means of two applications to real data sets.     

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

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 three-parameter extension of the log-logistic distribution with applications to survival data

In this article, a new three-parameter extension of the two-parameter log-logistic distribution is introduced. Several distributional properties such as moment-generating function, quantile function, mean residual lifetime, the Renyi and Shanon entropies, and order statistics are considered. The estimation of the model parameters for complete and right-censored cases is investigated competently by maximum likelihood estimation (MLE). A simulation study is conducted to show that these MLEs are consistent in moderate samples. Two real datasets are considered; one is a right-censored data to show that the proposed model has a superior performance over several existing popular models.     

A bimodal flexible distribution for lifetime data

ABSTRACT

A four-parameter extended bimodal lifetime model called the exponentiated log-sinh Cauchy distribution is proposed. It extends the log-sinh Cauchy and folded Cauchy distributions. We derive some of its mathematical properties including explicit expressions for the ordinary moments and generating and quantile functions. The method of maximum likelihood is used to estimate the model parameters. We implement the fit of the model in the GAMLSS package and provide the codes. The flexibility of the model is illustrated by means of three real data sets.     

The Poisson-X family of distributions

ABSTRACT

Recently, Risti? and Nadarajah [A new lifetime distribution. J Stat Comput Simul. 2014;84:135–150] introduced the Poisson generated family of distributions and investigated the properties of a special case named the exponentiated-exponential Poisson distribution. In this paper, we study general mathematical properties of the Poisson-X family in the context of the T-X family of distributions pioneered by Alzaatreh et al. [A new method for generating families of continuous distributions. Metron. 2013;71:63–79], which include quantile, shapes of the density and hazard rate functions, asymptotics and Shannon entropy. We obtain a useful linear representation of the family density and explicit expressions for the ordinary and incomplete moments, mean deviations and generating function. One special lifetime model called the Poisson power-Cauchy is defined and some of its properties are investigated. This model can have flexible hazard rate shapes such as increasing, decreasing, bathtub and upside-down bathtub. The method of maximum likelihood is used to estimate the model parameters. We illustrate the flexibility of the new distribution by means of three applications to real life data sets.