Characterizations of New Modified Weibull Distribution

Several characterizations of a New Modified Weibull distribution, introduced by Doostmoradi et al. (2014), are presented. These characterizations are based on: (i) truncated moment of a function of the random variable; (ii) the hazard function; (iii) a single function of the random variable; (iv) truncated moment of certain function of the 1st order statistic

Concept of Sub-Independence

Limit theorems as well as other well-known results in probability and statistics are often based on the distributions of the sums of independent random variables. The concept of sub-independence, which is weaker than that of independence, is shown to be sufficient to yield the conclusions of these theorems and results. It also provides a measure of dissociation between two random variables which is stronger than uncorrelatedness

Characterizations of Distributions of Ratio of Certain Independent Random Variables

Various characterizations of the distributions of the ratio of two independent gamma and exponential random variables as well as that of two independent Weibull random variables are presented. These characterizations are based, on a simple relationship between two truncated moments ; on hazard function ; and on functions of order statistics

Characterizations of Distribution of Ratio of Rayleigh Random Variables

Various characterizations of the distribution of the ratio of two independent Rayleigh random variables are presented. These characterizations are based, on a truncated moment; on hazard function; and on certain functions of order statistics

Characterizations of Gamma Distribution via Sub-Independent Random Variables

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. Inspired by the excellent work of Jin and Lee (2014), we present certain characterizations of gamma distribution based on the concept of sub-independence

Various Characterizations of Modified Weibull and Log Modified Distributions

Various characterizations of the well-known modifiedWeibull and log-modifiedWeibull distributions are presented. These characterizations are based on a simple relationship between two truncated moments; on the hazard function and on functions of the order statistics

Some Remarks on Recent Characterizations of Continuous Distributions

We would closely look at two recent published papers dealing with characterizations of certain univariate continuous distributions. We shall explain that the main results reported lack important assumptions. These results nevertheless are based on the conditional expectations of monotone functions of the generalized order statistics. We will also mention that similar results have recently been reported without the assumption of monotonicity of the functions of the generalized order statistics

Characterizations and Infinite Divisibility of Certain Recently Introduced Distributions IV

Certain characterizations of recently proposed univariate continuous distributions are presented in different directions. This work contains a good number of reintroduced distributions and may serve as a source of preventing the reinvention and/or duplication of the existing distributions in the future

Characterization of Bimodal Extension of the Generalized Gamma Distribution

Cankaya et al. (2015) [1] introduced a bimodal extension of the generalized gamma distribution and studied certain properties and ap­plicability of this distribution. This is a continuous distribution whose probability density function is defined via two branches. These types of distributions are very interesting but not easy to characterize. In this short note we try to present a characterization of this distribution which we believe, it may possibly be the only one for this rather complicated distribution