Characterizations of Certain Continuous Univariate Distributions Based on the Conditional Distribution of Generalized Order Statistics

The problem of characterizing probability distributions is an interesting problem which has recently attracted the attention of many researchers. Various characterization results have been established in different directions as reported in the literature. We present here, various characterizations of certain univariate continuous distributions based on the conditional distribution of generalized order statistics

Characterizations of Pareto, Weibull and Power Function Distributions Based On Generalized Order Statistics

Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterization of Pareto and Weibull distributions based on the conditional expectation of generalized order statistics extending the characterization results reported by Jin and Lee (2014). We also present a characterization of the power function distribution based on the conditional expectation of lower generalized order statistics

Characterizations of Distributions via Conditional Expectation of Generalized Order Statistics

Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterizations of certain continuous distributions based on the conditional expectation of generalized order statistics

On Order Statistics for GS-Distributions

In this article, a class of distributions is used to establish several recurrence relations satisfied by single and product moments of order statistics and progressive Type-II right censoring. The recurrence relations for moments of some specific distributions including uniform (a;b); exponential (λ); generalized exponential (α;λ;ν); beta (1;b); beta (b;1); logistic (α;β) and other distributions from order statistics and progressive Type-II right censoring can be obtained as special cases. A short explanation of GS-distribution can be found in reference [27]. As an example, means, variances and covariances for standard exponential distribution of progressive Type-II right censored order statistics are computed. Various characterizations of the recently introduced GS-distributions are presented. These characterizations are based on a simple relationship between two truncated moments ; on hazard function ; and on functions of order statistics. A characterization of the GS-distributions based on conditional moment of order statistics is extended to truncated moment of order statistics

Characterizations of Levy Distribution via Sub-Independence of the Random Variables and Truncated Moments

The concept of sub-independence is based on the convolution of the distributions of the random variables. It is much weaker than that of independence, but is shown to be sufficient to yield the conclusions of important theorems and results in probability and statistics. It also provides a measure of dissociation between two random variables which is much stronger than uncorrelatedness. Following Ahsanullah and Nevzorov (2014), we present certain characterizations of Levy distribution based on: (i) the sub-independence of the random variables; (ii) a simple relationship between two truncated moments; (iii) conditional expectation of certain function of the random variable. In case of independence, characterization (i) reduces to that of Ahsanullah and Nevzorov (2014)

New Flexible Regression Models Generated by Gamma Random Variables with Censored Data

We propose and study a new log-gamma Weibull regression model. We obtain explicit expressions for the raw and incomplete moments, quantile and generating functions and mean deviations of the log-gamma Weibull distribution. We demonstrate that the new regression model can be applied to censored data since it represents a parametric family of models which includes as sub-models several widely-known regression models and therefore can be used more effectively in the analysis of survival data. We obtain the maximum likelihood estimates of the model parameters by considering censored data and evaluate local influence on the estimates of the parameters by taking different perturbation schemes. Some global-influence measurements are also investigated. Further, for different parameter settings, sample sizes and censoring percentages, various simulations are performed. In addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We demonstrate that our extended regression model is very useful to the analysis of real data and may give more realistic fits than other special regression models

New Classes of Univariate Continuous Exponential Power Series Distributions

Recently, many researchers have developed various classes of continuous probability distributions which can be generated via the generalized Pearson differential equation and other techniques. In this paper, motivated by the importance of the power series in probability theory and its applications, we derive some new classes of univariate exponential power series distributions for a realvalued continuous random variable, which we call exponential power series distributions. Various mathematical properties of the proposed classes of distributions are discussed. Based on these distributional properties, we have established some characterizations of these distributions as well. It is hoped that the findings of the paper will be useful for researchers in the fields of probability, statistics and other applied sciences