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The gamma-uniform distribution and its applications

Hamzeh Torabi, Narges Montazeri Hedesh (2012)

Kybernetika

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 generalized FGM distribution and its application to stereology of extremes

Daniel Hlubinka, Samuel Kotz (2010)

Applications of Mathematics

The generalized FGM distribution and related copulas are used as bivariate models for the distribution of spheroidal characteristics. It is shown that this model is suitable for the study of extremes of the 3D spheroidal particles observed in terms of their random planar sections.

The Heyde theorem on a-adic solenoids

Margaryta Myronyuk (2013)

Colloquium Mathematicae

We prove the following analogue of the Heyde theorem for a-adic solenoids. Let ξ₁, ξ₂ be independent random variables with values in an a-adic solenoid Σ a and with distributions μ₁, μ₂. Let α j , β j be topological automorphisms of Σ a such that β ₁ α - 1 ₁ ± β ₂ α - 1 ₂ are topological automorphisms of Σ a too. Assuming that the conditional distribution of the linear form L₂ = β₁ξ₁ + β₂ξ₂ given L₁ = α₁ξ₁ + α₂ξ₂ is symmetric, we describe the possible distributions μ₁, μ₂.

The importance of being the upper bound in the bivariate family.

Carles M. Cuadras (2006)

SORT

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 integrated squared error estimation of parameters.

Jamal-Dine Chergui (1996)

Extracta Mathematicae

This paper deals with the problem of estimation in the parametric case for discrete random variables. Their study is facilitated by the powerful method of probability generating function.

The inverse distribution for a dichotomous random variable

Elisabetta Bona, Dario Sacchetti (1997)

Commentationes Mathematicae Universitatis Carolinae

In this paper we will deal with the determination of the inverse of a dichotomous probability distribution. In particular it will be shown that a dichotomous distribution admit inverse if and only if it corresponds to a random variable assuming values ( 0 , a ) , a ∈ ℝ + . Moreover we will provide two general results about the behaviour of the inverse distribution relative to the power and to a linear transformation of a measure.

The LASSO estimator: Distributional properties

Rakshith Jagannath, Neelesh S. Upadhye (2018)

Kybernetika

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 law of the iterated logarithm for the multivariate kernel mode estimator

Abdelkader Mokkadem, Mariane Pelletier (2003)

ESAIM: Probability and Statistics

Let θ be the mode of a probability density and θ n its kernel estimator. In the case θ is nondegenerate, we first specify the weak convergence rate of the multivariate kernel mode estimator by stating the central limit theorem for θ n - θ . Then, we obtain a multivariate law of the iterated logarithm for the kernel mode estimator by proving that, with probability one, the limit set of the sequence θ n - θ suitably normalized is an ellipsoid. We also give a law of the iterated logarithm for the l p norms, p ∈ [ 1 , ∞ ] , of θ n - θ ....

The law of the iterated logarithm for the multivariate kernel mode estimator

Abdelkader Mokkadem, Mariane Pelletier (2010)

ESAIM: Probability and Statistics

Let θ be the mode of a probability density and θn its kernel estimator. In the case θ is nondegenerate, we first specify the weak convergence rate of the multivariate kernel mode estimator by stating the central limit theorem for θn - θ. Then, we obtain a multivariate law of the iterated logarithm for the kernel mode estimator by proving that, with probability one, the limit set of the sequence θn - θ suitably normalized is an ellipsoid. We also give a law of the iterated logarithm for the...

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