K-distribution

About: K-distribution is a research topic. Over the lifetime, 1281 publications have been published within this topic receiving 51774 citations.

Review on Some G-Family Distributions

Abstract: In this thesis we study the properties of some G-family of distributions, such as, Kumaraswamy-G family, Zografos-Balakrishnan-G family and Ristic-Balakrishnan-G family for any continuous baseline G distribution. Here, we provide a thorough study of general mathematical properties of these family of distributions. We are trying to find out some new distributions by making use of the families demonstrated. We discuss the properties of Zografos-Balakrishnan-generalized exponential distribution, such as, probability density function (pdf), cumulative distribution function (cdf), hazard rate function, moments, quantile function, entropy and estimation of the parameters by maximum likelihood method.

Maxima of Weibull-like distributions and the Lambert W function

Abstract: The Weibull--like distributions form a large class of probability distributions that belong to the domain of attraction for the maxima of the Gumbel law. Besides the Weibull distribution, it includes important distributions as the Gamma laws and, in particular, the $\chi^2$ distributions. In order to have explicit expressions of the norming constants for the maxima it is necessary to solve asymptotically a nonlinear equation; however, for some members of that family, numerical and simulation studies show that the constants that are usual suggested are inaccurate for moderate or even large sample sizes. In this paper we propose other norming constants computed with the asymptotics of the Lambert W function that significantly improve the accuracy of the approximation to the Gumbel law. These results are applied to the computation of the constants for the maxima of Gamma random variables that appear in some applied problems.

And their applications

Abstract: Link (American Statistician, 35 (1981), pp. 44-46) described a method of deriving the moments of some well known discrete probability distributions using finite difference operators. Rao and Janardan (American Statistician, 36 (1982), pp. 381-383) applied this method to derive the moments of two classes of multi-variate discrete distributions, namely the generalized power series distribution and the unified multivariate hypergeometric distribution. In this paper two other classes of distributions are con- sidered-the factorial series distributions (Berg (Scand. J. Statist., 1 (1974), pp. 145-152; 3 (1976), pp. 86-88)) and the modified power series distributions (Gupta (Sankhya, Ser. B, 35 (1974), pp. 288-298)). The results of Link follow as special cases. The probability generating function of the committee members distribution is also given. The minimum chi-square estimators of the generalized Poisson distribution are 1. Introduction. Recently, Link derived compact and elegant expressions for the moments of several well-known discrete distributions using finite difference operators, such as the binomial, Poisson, geometric and hypergeometric distributions. Rao and Janardan (1981) obtained expressions for the general mixed moments of the multivari- ate generalized power series distribution and the unified multivariate hypergeometric distribution and those of multinomial, negative multinomial, hypergeometric and multivariate Polya distributions as special cases. Computation of general moments is very often cumbersome and the final form is not quite simple. This is the case for two classes of series distributions considered in this paper. The advantage of the method which utilizes finite difference operators is that the general moments may be obtained directly rather than going through the factorial moments. More specifically, in this paper we consider the moments of the Factorial Series Distributions (FSD) introduced by Berg (1974), (1976) and the Modified Power Series Distributions (MPSD) introduced by Gupta (1974), as given in the following definitions. DEFINITION 1. A discrete random variable (r.v.) X is said to have an FSD if its probability function (p.f.) is given by

Some Functionals and Approximation Operators Associated with a Family of Discrete Probability Distributions

Abstract: A certain discrete probability distribution was considered in ["A discrete probability distribution and some applications", Mediterr. J. Math., 2023]. Its basic properties were investigated and some applications were presented. We now embed this distribution into a family of discrete distributions depending on two parameters and investigate the properties of the new distributions.