Related papers: Random convolution of inhomogeneous distributions …
In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…
Kagan and Shalaevski 1967 have shown that if the random variables $X_1,\dots,X_n$ are independent and identically distributed and the distribution of $\sum_{i=1}^n(X_i+a_i)^2$ $a_i\in \mathbb{R}$ depends only on $\sum_{i=1}^na_i^2$ , then…
Let $\eta_1$, $\eta_2,\ldots$ be independent copies of a random variable $\eta$ with zero mean and finite variance which is bounded from the right, that is, $\eta\leq b$ almost surely for some $b>0$. Considering different types of the…
We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the…
Multiplicative self-decomposable laws describe random variables that can be decomposed into a product of a scaled-down version of themselves and an independent residual term. Shanbhag et al.~(1977) have shown that the gamma distribution is…
We define in a probabilistic way a parametric family of multivariate extreme value distributions. We derive its copula, which is a mixture of several complete dependent copulas and total independent copulas, and the bivariate tail…
A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…
A bivariate random vector can exhibit either asymptotic independence or dependence between the largest values of its components. When used as a statistical model for risk assessment in fields such as finance, insurance or meteorology, it is…
We establish some asymptotic expansions for infinite weighted convolution of distributions having regular varying tails. Various applications to statistics and probability are developed.
We take an $L_1$-dense class of functions $\Cal F$ on a measurable space $(X,\Cal X)$ and a sequence of i.i.d. $X$-valued random variables $\xi_1,\dots,\xi_n$, and give a good estimate on the tail behaviour of $\sup\limits_{f\in\Cal…
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…
Some new survival distributions are introduced based on a generalised exponential function. This class of distributions includes heavy-tailed generalisations of exponential, Weibull and gamma distributions. Properties of the distributions…
In this note a two sided bound on the tail probability of sums of independent, and either symmetric or nonnegative, random variables is obtained. We utilize a recent result by Lata{\l}a on bounds on moments of such sums. We also give a new…
We give explicit bounds for the tail probabilities for sums of independent geometric or exponential variables, possibly with different parameters.
We give an explicit realization of the $\eta$-convolution power of an $A$-valued distribution, as defined earlier by Anshelevich, Belinschi, Fevrier and Nica. If $\eta:A\to A$ is completely positive and $\eta\geq\operatorname{id}$, we give…
Let $\{X_i,i\geq1\}$ be a sequence of negatively associated random variables, and let $\{X_i^\ast,i\geq 1\}$ be a sequence of independent random variables such that $X_i^\ast$ and $X_i$ have the same distribution for each $i$. Denote by…
We study the exponential functional $\int_0^\infty e^{-\xi_{s-}} \, d\eta_s$ of two one-dimensional independent L\'evy processes $\xi$ and $\eta$, where $\eta$ is a subordinator. In particular, we derive an integro-differential equation for…
We derive in this short report the exact exponential decreasing tail of distribution for naturel normed sums of independent centered random variables (r.v.), applying the theory of Grand Lebesgue Spaces (GLS). We consider also some…
Considered a pair of random lifetimes whose dependence is described by a Time Transformed Exponential model, we provide analytical expressions for the distribution of their sum. These expressions are obtained by using a representation of…
We construct a non - improved exponential bounds for distribution of normed sums of i.,i.d. random variables with random numbers of summand.