Tail orderings and the total time on test transform
The paper presents some connections between two tail orderings of distributions and the total time on test transform. The procedure for testing the pure-tail ordering is proposed.
The beta Gumbel distribution.
The Bivariate Non-central Negative Binomial Distributions.
The effect of Gaussian blurring on the extraction of peaks and pits from digital elevation models.
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 Heyde theorem on a-adic solenoids
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 and with distributions μ₁, μ₂. Let be topological automorphisms of such that are topological automorphisms of 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 inverse distribution for a dichotomous random variable
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 , . 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 Lukacs-Olkin-Rubin theorem without invariance of the "quotient"
The Lukacs theorem is one of the most brilliant results in the area of characterizations of probability distributions. First, because it gives a deep insight into the nature of independence properties of the gamma distribution; second, because it uses beautiful and non-trivial mathematics. Originally it was proved for probability distributions concentrated on (0,∞). In 1962 Olkin and Rubin extended it to matrix variate distributions. Since that time it has been believed that the fundamental reason...
The Relationship Between Moments of Truncated and Original Distributions Plus Some Other Simple Structural Properties of Weighted Distributions.
The relevation transform and a generalization of the gamma distribution function
The role of functional equations in stochastic model building.
Transformationen, die die Normalverteilung charakterisieren.
Tree and local computations in a cross–entropy minimization problem with marginal constraints
In probability theory, Bayesian statistics, artificial intelligence and database theory the minimum cross-entropy principle is often used to estimate a distribution with a given set of marginal distributions under the proportionality assumption with respect to a given “prior” distribution . Such an estimation problem admits a solution if and only if there exists an extension of that is dominated by . In this paper we consider the case that is not given explicitly, but is specified as the...
Two families of normality tests based on Polya characterization, and their efficiency.