Class Of Continuous Distributions Research Articles

Generating New Flexible Lifetime Class of Distributions Based on Competing Risks and Frailty Models

New classes of continuous distributions have been generated, in the last decad, based on a compounding procedure arises on a latent competing risks problem. This procedure assumes the homogeneity between the population individuals. In this paper, a new lifetime distribution is generated, assuming the heterogeneity at both population and individual levels, called Extended Gamma Gompertz (EGG) distribution. This distribution shows very desirable exibility of its hazard function. Some properties of the proposed distribution are given. Maximum likelihood estimation technique is used to estimate the parameters. A simulation study is performed to examine the performance of the proposed model. Finally, application to a real data set is given to exemplify the utility of the EGG distribution.

A Study on A New Type 1 Half-Logistic Family of Distributions and Its Applications

In this paper, we propose a new class of continuous distributions with two extra shape parameters called the a new type I half logistic-G family of distributions. Some of important properties including ordinary moments, quantiles, moment generating function, mean deviation, moment of residual life, moment of reversed residual life, order statistics and extreme value are obtained. To estimate the model parameters, the maximum likelihood method is also applied by means of Monte Carlo simulation study. A new location-scale regression model based on the new type I half logistic-Weibull distribution is then introduced. Applications of the proposed family is demonstrated in many fields such as survival analysis and univariate data fitting. Empirical results show that the proposed models provide better fits than other well-known classes of distributions in many application fields.

The generalized odd Burr III family of distributions: properties, applications and characterizations

ABSTRACTA new class of continuous distributions with two extra shape parameters is introduced named the generalized odd Burr III (GOBIII) family of distributions. The expression of density can be written as a linear combination of exponentiated densities related to baseline model. The basic properties such as ordinary moments, quantile and generating functions, two entropy measures and order statistics are derived. Three special models of proposed family are presented. Characterizations related to truncated moments and hazard function for GOBIII-G distribution are derived. Method of maximum likelihood is used to estimate the model parameters. We study the behaviour of the estimators by means of simulations. The importance of the new family is illustrated using two real data sets. The real data applications suggest that this family can provide better fits than other competitive distributions. The significance of GOBIII-G family lies in its capability to fit symmetric as well as skewed type of data.

Type II General Exponential Class of Distributions

In this paper, a new class of continuous distributions with two extra positive parameters is introduced and is called the Type II General Exponential (TIIGE) distribution. Some special models are presented. Asymptotics, explicit expressions for the ordinary and incomplete moments, moment residual life, reversed residual life, quantile and generating functions and stress-strengh reliability function are derived. Characterizations of this family are obtained based on truncated moments, hazard function, conditional expectation of certain functions of the random variable are obtained. The performance of the maximum likelihood estimators in terms of biases, mean squared errors and confidence interval length is examined by means of a simulation study. Two real data sets are used to illustrate the application of the proposed class.

The Nontransitivity Problem for Three Continuous Random Variables

The nontransitivity problem of the stochastic precedence relation for three independent random variables with distributions from a given class of continuous distributions is studied. Originally, this issue was formulated in one problem of strength theory. In recent time, nontransitivity has become a popular topic of research for the so-called nontransitive dice. Some criteria are first developed and then applied for proving that nontransitivity may not hold for many classical continuous distributions (uniform, exponential, Gaussian, logistic, Laplace, Cauchy, Simpson, one-parameter Weibull and others). The case of all distributions with a polynomial density on the unit interval is considered separately. Some promising directions of further investigations on the subject are outlined.

The Odd Log-Logistic Poisson-G Family of Distributions

We propose a new class of continuous distributions with two extra shape parameters named the Odd Log-Logistic Poisson -G family. Some of its mathematical properties including moments, quantile and generating functions and order statistics are obtained. We estimate the model parameters by the maximum likelihood method and present a Monte Carlo simulation study. The importance of the proposed family is demonstrated by means of three real data applications. Empirical results indicate that proposed family provides better fits than other well-known classes of distributions in real applications.

A note on the Cauchy-type mixture distributions

ABSTRACTAn interesting class of continuous distributions, called Cauchy-type mixture, with potential applications in modelling erratic phenomena is introduced by Soltani and Tafakori [A class of continuous kernels and Cauchy type heavy tail distributions. Statist Probab Lett. 2013;83:1018–1027]. In this work, we provide more insights into the Cauchy-type mixture distributions, involving certain characterizations, connections with the generalized Linnik distributions and the class of discrete distributions induced by stable laws. We also prove that the Laplace transform of Cauchy-type mixture distributions when normalized by constant terms become as a density functions in terms of distributional conjugate property.

Exponentiated Marshall-Olkin family of distributions

We study general mathematical properties of a new class of continuous distributions with three extra shape parameters called the exponentiated Marshal-Olkin family of distributions. Further, we present some special models of the new class and investigate the shapes and derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions and probability weighted moments. We discuss the estimation of the model parameters by maximum likelihood and show empirically the potentiality of the family by means of two applications to real data.

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

ABSTRACTWe 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 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.

ON CHARACTERIZATIONS OF CONTINUOUS DISTRIBUTIONS BY CONDITIONAL EXPECTATIONS OF UPPER RECORD VALUES

In this paper, general classes of continuous distributions are characterized by considering the conditional expectations of functions of upper record statistics. The specific distribution considered as a particular case of the general class of distribution are Exponential, Exponential Power(EP), Inverse Weibull, Beta Gumbel, Modified Weibull(MW), Weibull, Pareto, Power, Singh-Maddala, Gumbel, Rayleigh, Gompertz, Extream value 1, Beta of the first kind, Beta of the second kind and Lomax.

On Bayesian interval prediction of future generalized-order statistics using doubly censoring

Based on a one-sample scheme, general Bayesian prediction intervals (BPI) for future generalized-order statistics are obtained when the previous and future samples are assumed to follow a general class of continuous distributions. The prior belief of the experimenter is measured by two distributions according to whether one (two) parameter(s) is (are) unknown. BPI for upper-order statistics and upper record values are obtained as special cases. Doubly Type II censored of the observed data has been used here. Application to the Weibull (θ1, θ2) model is illustrated when θ1 is an unknown parameter and when both θ1 and θ2 are unknown parameters. Numerical computations are made when θ1 is unknown to illustrate the procedures.

An inverse problem for a class of continuous distributions with skewness

An inverse problem pertaining a class of univariate continuous distributions with skewness is investigated. The Fourier transform and analytic characteristic functions are used to obtain the results.

Permutation tests — A revival?!

It is shown that permutation tests have optimum properties for interesting classes of continuous distributions as well as for discrete ones. General conditions sufficient for uniformly maximal power on subclasses are given. Moreover, a variety of examples is presented.

A target distribution model for nonparametric density estimation

In this paper a model is proposed which represents a wide class of continuous distributions. It is shown how the parameters of this model can be estimated leading to a distribution estimator and a corresponding density estimator. An important property of this estimator is that it can be structured to reflect a priori knowledge of the unknown distribution. Finally, some examples are shown and some comparisons made with kernel and orthogonal series estimators.

A property of the mean deviation for a class of continuous distributions

A property of the mean deviation for a class of continuous distributions

A Property of the Mean Deviation for a Class of Continuous Distributions

A Property of the Mean Deviation for a Class of Continuous Distributions

On the coefficient of correlation for continuous distributions

Abstract 1. The use — and misuse — of the coefficient of correlation continues to give rise to much discussion among statisticians. 1 In spite of this, it cannot be expected that this measure of dependence between statistical variables will be abandoned in cases where it may be presumed that the distribution is normal in both variables (» Bravais' formula»), because in that case the measure satisfies all reasonable demands. It seems therefore worth while to point out that a much more comprehensive class of continuous distributions exists where the significance of the coefficient of correlation is the same as in the case of normal distribution. Before doing so we will, however, reconsider the case of normal correlation.