Extended Lindley Poisson Distribution

The Extended Lindley Poisson (ELP) distribution which is an extension of the extended Lindley distribution [2] is introduced and its properties are explored. This new distribution represents a more flexible model for the lifetime data. Some statistical properties of the proposed distribution including the shapes of the density, hazard rate functions, moments, Bonferroni and Lorenz curves are explored. Entropy measures and the distribution of the order statistics are given. The maximum likelihood estimation technique is used to estimate the model parameters and a simulation study is conducted to investigate the performance of the maximum likelihood estimates. Finally, we present applications of the model with a real data set to illustrate the usefulness of the proposed distribution

Kumaraswamy Lindley-Poisson Distribution: Theory and Applications

The Kumaraswamy Lindley-Poisson (KLP) distribution which is an extension of the Lindley-Poisson Distribution [21] is introduced and its properties are explored. This new distribution represents a more flexible model for the lifetime data. Some statistical properties of the proposed distribution including the shapes of the density and hazard rate functions are explored. Moments, entropy measures and the distribution of the order statistics are given. The maximum likelihood estimation technique is used to estimate the model parameters and a simulation study is conducted to investigate the performance of the maximum likelihood estimates. Finally some applications of the model with real data sets are presented to illustrate the usefulness of the proposed distribution

The Beta Lindley-Poisson Distribution with Applications

The beta Lindley-Poisson (BLP) distribution which is an extension of the Lindley-Poisson Distribution is introduced and its properties are explored. This new distribution represents a more flexible model for the lifetime data. Some statistical properties of the proposed distribution including the expansion of the density function, hazard rate function, moments and moment generating function, skewness and kurtosis are explored. Renyi entropy and the distribution of the order statistics are given. The maximum likelihood estimation technique is used to estimate the model parameters and finally applications of the model to real data sets are presented for the illustration of the usefulness of the proposed distribution

A New Class of Generalized Power Lindley Distribution with Applications to Lifetime Data

A new class of distribution called the beta-exponentiated power Lindley (BEPL) distribution is proposed. This class of distributions includes the Lindley (L), exponentiated Lindley (EL), power Lindley (PL), exponentiated power Lindley (EPL), beta-exponentiated Lindley (BEL), beta-Lindley (BL), and beta-power Lindley distributions (BPL) as special cases. Expansion of the density of BEPL distribution is obtained. Some mathematical properties of the new distribution including hazard function, reverse hazard function, moments, mean deviations, Lorenz and Bonferroni curves are presented. Entropy measures and the distribution of the order statistics are given. The maximum likelihood estimation technique is used to estimate the model parameters. Finally, real data examples are discussed to illustrate the usefulness and applicability of the proposed distribution

Generalized Topp-Leone-G power series class of distributions: properties and applications

This note is concerned with the construction, development and applications of a new class of distributions referred to as the Generalized Topp-Leone-G Power Series class of distributions. More importantly, this new generalized class of distributions can be expressed as an infinite linear combination of exponentiated-G distributions, which allows us to develop and obtain the important statistical and mathematical properties. Monte Carlo simulations are conducted to established the consistency of the estimation process. Applications in several areas are presented to illustrate the importance and usefulness of this new class of distributions

The Log-Logistic Weibull Distribution with Applications to Lifetime Data

In this paper, a new generalized distribution called the log-logistic Weibull (LLoGW) distribution is developed and presented. This distribution contain the log-logistic Rayleigh (LLoGR), log-logistic exponential (LLoGE) and log-logistic (LLoG) distributions as special cases. The structural properties of the distribution including the hazard function, reverse hazard function, quantile function, probability weighted moments, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, distribution of order statistics, L-moments and Renyi entropy are derived. Method of maximum likelihood is used to estimate the parameters of this new distribution. A simulation study to examine the bias, mean square error of the maximum likelihood estimators and width of the condence intervals for each parameter is presented. Finally, real data examples are presented to illustrate the usefulness and applicability of the model

A Generalization of LASSO Modeling via Bayesian Interpretation

The aim of this paper is to introduce a generalized LASSO regression model that is derived using a generalized Laplace (GL) distribution. Five different GL distributions are obtained through the T -R{Y } framework with quantile functions of standard uniform, Weibull, log-logistic, logistic, and extreme value distributions. The properties, including quantile function, mode, and Shannon entropy of these GL distributions are derived. A particular case of GL distributions called the beta-Laplace distribution is explored. Some additional components to the constraint in the ordinary LASSO regression model are obtained through the Bayesian interpretation of LASSO with beta-Laplace priors. The geometric interpretations of these additional components are presented. The effects of the parameters from beta-Laplace distribution in the generalized LASSO regression model are also discussed. Two real data sets are analyzed to illustrate the flexibility and usefulness of the generalized LASSO regression model in the process of variable selection with better prediction performance. Consequently, this research study demonstrates that more flexible statistical distributions can be used to enhance LASSO in terms of flexibility in variable selection and shrinkage with better prediction

Dagum-Poisson Distribution: Model, Properties and Application

A new four parameter distribution called the Dagum-Poisson (DP) distribution is introduced and studied. This distribution is obtained by compounding Dagum and Poisson distributions. The structural properties of the new distribution are discussed, including explicit algebraic formulas for its survival and hazard functions, quantile function, moments, moment generating function, conditional moments, mean and median deviations, Bonferroni and Lorenz curves, distribution of order statistics and R\\u27enyi entropy. Method of maximum likelihood is used for estimating the model parameters. A Monte Carlo 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. A real data set is used to illustrate the usefulness, applicability, importance and flexibility of the new distribution

Exponentiated Power Lindley Poisson Distribution: Properties and Applications

A new four-parameter distribution called the exponentiated power Lindley-Poisson (EPLP) distribution which is an extension of the power Lindley and Lindley-Poisson distributions is introduced. Statistical properties of the distribution including the shapes of the density and hazard functions, moments, entropy measures and distribution of order statistics are given. Maximum likelihood estimation technique is used to estimate the 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. Finally applications to real data sets are presented to illustrate the usefulness of the proposed distribution

A New Compound Class of Log-Logistic Weibull Poisson Distribution: 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