Wrapped Lindley distribution

In this article, we introduce a new circular distribution to be called as wrapped Lindley distribution and derive expressions for characteristic function, trigonometric moments, coefficients of skewness, and kurtosis. Method of maximum likelihood estimation is used for the estimation of parameters. We carry out a simulation study to show that the obtained maximum likelihood estimator is consistent. The proposed model is also applied to a real-life dataset, and its performance is compared with that of wrapped exponential distribution.     

Modified slashed-Rayleigh distribution

A new family of slash distributions, the modified slashed-Rayleigh distribution, is proposed and studied. This family is an extension of the ordinary Rayleigh distribution, being more flexible in terms of distributional kurtosis. It arises as a quotient of two independent random variables, one being a Rayleigh distribution in the numerator and the other a power of the exponential distribution in denominator. We present properties of the proposed family. In addition, we carry out estimation of the model parameters by moment and maximum likelihood methods. Finally, we conduct a small-scale simulation study to evaluate the performance of the maximum likelihood estimators and apply the results to a real data set, revealing its good performance.     

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.     

A new absolute continuous bivariate generalized exponential distribution

The generalized exponential is the most commonly used distribution for analyzing lifetime data. This distribution has several desirable properties and it can be used quite effectively to analyse several skewed life time data. The main aim of this paper is to introduce absolutely continuous bivariate generalized exponential distribution using the method of Block and Basu (1974). In fact, the Block and Basu exponential distribution will be extended to the generalized exponential distribution. We call the new proposed model as the Block and Basu bivariate generalized exponential distribution, then, discuss its different properties. In this case the joint probability distribution function and the joint cumulative distribution function can be expressed in compact forms. The model has four unknown parameters and the maximum likelihood estimators cannot be obtained in explicit form. To compute the maximum likelihood estimators directly, one needs to solve a four dimensional optimization problem. The EM algorithm has been proposed to compute the maximum likelihood estimations of the unknown parameters. One data analysis is provided for illustrative purposes. Finally, we propose some generalizations of the proposed model and compare their models with each other.     

Slashed generalized exponential distribution

In this paper, we introduce an extension of the generalized exponential (GE) distribution, making it more robust against possible influential observations. The new model is defined as the quotient between a GE random variable and a beta-distributed random variable with one unknown parameter. The resulting distribution is a distribution with greater kurtosis than the GE distribution. Probability properties of the distribution such as moments and asymmetry and kurtosis are studied. Likewise, statistical properties are investigated using the method of moments and the maximum likelihood approach. Two real data analyses are reported illustrating better performance of the new model over the GE model.     

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.     

Inference for IZAWA’S Bivariate Gamma Distribution

Abstract

In this article, we aim to establish some theoretical properties of Izawa’s bivariate gamma distribution having equal shape parameters. First, we propose a procedure to obtain the maximum likelihood estimates and derive an expression for the Fisher information. Simulation studies illuminate the properties of maximum likelihood estimators. We also establish an asymptotic test for independence based on the limiting distribution of maximum likelihood estimators.     

A new class of distribution having decreasing,increasing, and bathtub-shaped failure rate

In this article, we propose a new class of distribution which is based on the concept of exponentiated generalization with some modification so as to provide a better result in terms of flexibility. Our proposed distribution accommodates various shapes of hazard rate including the bathtub. Exponential distribution has been taken as the baseline distribution. Various statistical properties of the proposed distribution have been studied. We have used the method of maximum likelihood for estimation of the parameters of the proposed model. Last, we have analyzed four real datasets to illustrate the flexibility of the model in comparison to eight existing well-known distributions.     

Slashed generalized Rayleigh distribution

We introduce a new family of distributions suitable for fitting positive data sets with high kurtosis which is called the Slashed Generalized Rayleigh Distribution. This distribution arises as the quotient of two independent random variables, one being a generalized Rayleigh distribution in the numerator and the other a power of the uniform distribution in the denominator. We present properties and carry out estimation of the model parameters by moment and maximum likelihood (ML) methods. Finally, we conduct a small simulation study to evaluate the performance of ML estimators and analyze real data sets to illustrate the usefulness of the new model.     

Reparameterization strategies for hidden Markov models and Bayesian approaches to maximum likelihood estimation

This paper synthesizes a global approach to both Bayesian and likelihood treatments of the estimation of the parameters of a hidden Markov model in the cases of normal and Poisson distributions. The first step of this global method is to construct a non-informative prior based on a reparameterization of the model; this prior is to be considered as a penalizing and bounding factor from a likelihood point of view. The second step takes advantage of the special structure of the posterior distribution to build up a simple Gibbs algorithm. The maximum likelihood estimator is then obtained by an iterative procedure replicating the original sample until the corresponding Bayes posterior expectation stabilizes on a local maximum of the original likelihood function.     

Opportunities of the minimum Anderson–Darling estimator as a variant of the maximum likelihood method

We reveal that the minimum Anderson–Darling (MAD) estimator is a variant of the maximum likelihood method. Furthermore, it is shown that the MAD estimator offers excellent opportunities for parameter estimation if there is no explicit formulation for the distribution model. The computation time for the MAD estimator with approximated cumulative distribution function is much shorter than that of the classical maximum likelihood method with approximated probability density function. Additionally, we research the performance of the MAD estimator for the generalized Pareto distribution and demonstrate a further advantage of the MAD estimator with an issue of seismic hazard analysis.     

Modified skew-slash distribution

Abstract

In this work, we introduce a new skewed slash distribution. This modification of the skew-slash distribution is obtained by the quotient of two independent random variables. That quotient consists on a skew-normal distribution divided by a power of an exponential distribution with scale parameter equal to two. In this way, the new skew distribution has a heavier tail than that of the skew-slash distribution. We give the probability density function expressed by an integral, but we obtain some important properties useful for making inferences, such as moment estimators and maximum likelihood estimators. By way of illustration and by using real data, we provide maximum likelihood estimates for the parameters of the modified skew-slash and the skew-slash distributions. Finally, we introduce a multivariate version of this new distribution.     

Generalized Inverse Gamma Distribution and its Application in Reliability

In this article, we introduce a new reliability model of inverse gamma distribution referred to as the generalized inverse gamma distribution (GIG). A generalization of inverse gamma distribution is defined based on the exact form of generalized gamma function of Kobayashi (1991). This function is useful in many problems of diffraction theory and corrosion problems in new machines. The new distribution has a number of lifetime special sub-models. For this model, some of its statistical properties are studied. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is derived. We also demonstrate the usefulness of this distribution on a real data set.     

The cosine geometric distribution with count data modeling

In this paper, a new two-parameter discrete distribution is introduced. It belongs to the family of the weighted geometric distribution (GD), with the feature of using a particular trigonometric weight. This configuration adds an oscillating property to the former GD which can be helpful in analyzing the data with over-dispersion, as developed in this study. First, we present the basic statistical properties of the new distribution, including the cumulative distribution function, hazard rate function and moment generating function. Estimation of the related model parameters is investigated using the maximum likelihood method. A simulation study is performed to illustrate the convergence of the estimators. Applications to two practical datasets are given to show that the new model performs at least as well as some competitors.     

A new lifetime model with regression models,characterizations and applications

In this article, we introduce a new extension of Burr XII distribution called Topp Leone Generated Burr XII distribution. We derive some of its properties. Useful characterizations are presented. Simulation study is performed to assess the performance of the maximum likelihood estimators. Censored maximum likelihood estimation is presented in the general case of multi-censored data. The new location-scale regression model based on the proposed distribution is introduced. The usefulness of the proposed models is illustrated empirically by means of three real datasets.     

Estimation for the Generalized Pareto Distribution Using Maximum Likelihood and Goodness of Fit

In this article, we introduce a new estimator for the generalized Pareto distribution, which is based on the maximum likelihood estimation and the goodness of fit. The asymptotic normality of the new estimator is shown and a small simulation. From the simulation, the performance of the new estimator is roughly comparable with maximum likelihood for positive values of the shape parameter and often much better than maximum likelihood for negative values.     

Multivariate normal mean-variance mixture distribution based on Lindley distribution

This article introduces a new asymmetric distribution constructed by assuming the multivariate normal mean-variance mixture model. Called normal mean-variance mixture of the Lindley distribution, we derive some mathematical properties of the new distribution. Also, a feasible maximum likelihood estimation procedure using the EM algorithm and the asymptotic standard errors of parameter estimates are developed. The performance of the proposed distribution is illustrated by means of real datasets and simulation analysis.     

Most Likely Transformations

We propose and study properties of maximum likelihood estimators in the class of conditional transformation models. Based on a suitable explicit parameterization of the unconditional or conditional transformation function, we establish a cascade of increasingly complex transformation models that can be estimated, compared and analysed in the maximum likelihood framework. Models for the unconditional or conditional distribution function of any univariate response variable can be set up and estimated in the same theoretical and computational framework simply by choosing an appropriate transformation function and parameterization thereof. The ability to evaluate the distribution function directly allows us to estimate models based on the exact likelihood, especially in the presence of random censoring or truncation. For discrete and continuous responses, we establish the asymptotic normality of the proposed estimators. A reference software implementation of maximum likelihood‐based estimation for conditional transformation models that allows the same flexibility as the theory developed here was employed to illustrate the wide range of possible applications.     

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.     

The Kumaraswamy GEV distribution

The popular generalized extreme value (GEV) distribution has not been a flexible model for extreme values in many areas. We propose a generalization – referred to as the Kumaraswamy GEV distribution – and provide a comprehensive treatment of its mathematical properties. We estimate its parameters by the method of maximum likelihood and provide the observed information matrix. An application to some real data illustrates flexibility of the new model. Finally, some bivariate generalizations of the model are proposed.