Tendency Towards Normality of Linear Combinations of Random Variables.
The characterization of discrete distributions by conditional distributions
The connection between the proximate order of an entire characteristic function and the corresponding distribution function
The distribution of the interval between events of a Cox process with shot noise intensity.
The distribution of the values of a random function in the unit disk
The gamma-uniform distribution and its applications
Up to present for modelling and analyzing of random phenomenons, some statistical distributions are proposed. This paper considers a new general class of distributions, generated from the logit of the gamma random variable. A special case of this family is the Gamma-Uniform distribution. We derive expressions for the four moments, variance, skewness, kurtosis, Shannon and Rényi entropy of this distribution. We also discuss the asymptotic distribution of the extreme order statistics, simulation issues,...
The geometric structure of the inverse gamma distribution.
The importance of being the upper bound in the bivariate family.
Any bivariate cdf is bounded by the Fréchet-Hoeffding lower and upper bounds. We illustrate the importance of the upper bound in several ways. Any bivariate distribution can be written in terms of this bound, which is implicit in logit analysis and the Lorenz curve, and can be used in goodness-of-fit assesment. Any random variable can be expanded in terms of some functions related to this bound. The Bayes approach in comparing two proportions can be presented as the problem of choosing a parametric...
The intersections of random finite sets
The Kolmogorov distance between the binomial and Poisson laws: efficient algorithms and sharp estimates.
The LASSO estimator: Distributional properties
The least absolute shrinkage and selection operator (LASSO) is a popular technique for simultaneous estimation and model selection. There have been a lot of studies on the large sample asymptotic distributional properties of the LASSO estimator, but it is also well-known that the asymptotic results can give a wrong picture of the LASSO estimator's actual finite-sample behaviour. The finite sample distribution of the LASSO estimator has been previously studied for the special case of orthogonal models....
The non-central g-distribution and its application
The range of a random function defined in the unit disk
The recurrence relations for the moments of the discrete probability distributions [Book]
The relevation transform and a generalization of the gamma distribution function
The use of fractional calculus in probability
Transformations groups of the Andersson-Perlman cone.
Transformations of copulas
Transformations of copulas by means of increasing bijections on the unit interval and attractors of copulas are discussed. The invariance of copulas under such transformations as well as the relationship to maximum attractors and Archimax copulas is investigated.
Two dimensional probabilities with a given conditional structure
A properly measurable set (where are Polish spaces and is the space of Borel probability measures on ) is considered. Given a probability distribution the paper treats the problem of the existence of -valued random vector for which and -almost surely that possesses moreover some other properties such as “ has the maximal possible support” or “’s are extremal...
Two lognormal models for real data.