Related papers: The variance-gamma product distribution
We consider two independent random variables with the given tail asymptotic (e.g. power or exponential). We find tail asymptotic for their sum and product. This is done by some cumbersome but purely technical computations and requires the…
The variance-gamma (VG) distributions form a four-parameter family which includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial modelling and distributional…
Dependency functions of dependent variables are relevant for i) performing uncertainty quantification and sensitivity analysis in presence of dependent variables and/or correlated variables, and ii) simulating random dependent variables. In…
The paper considers the distribution of a general linear combination of central and non-central chi-square random variables by exploring the branch cut regions that appear in the standard Laplace inversion process. Due to the original…
This is an expository note on useful expressions for the density function of a product of independent random variables where each variable has a Beta distribution.
In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
We study the analytical properties of the Laplace transform of the lognormal distribution. Two integral expressions for the analytic continuation of the Laplace transform of the lognormal distribution are provided, one of which takes the…
Stable distributions are an important class of infinitely-divisible probability distributions, of which two special cases are the Cauchy distribution and the normal distribution. Aside from a few special cases, the density function for…
The XGamma distribution is a generated distribution from a mixture of Exponential and Gamma distributions. It is found that in many cases the XGamma has more flexibility than the Exponential distribution. In this paper we consider the sum…
In this paper, we obtain some results on precise large deviations for non-random and random sums of widely dependent random variables with common dominatedly varying tail distribution or consistently varying tail distribution on…
In this paper, we study the value-distributions of $L$-functions of holomorphic primitive cusp forms in the level aspect. We associate such automorphic $L$-functions with probabilistic models called the random Euler products. First, we…
We discuss the product of $M$ rectangular random matrices with independent Gaussian entries, which have several applications including wireless telecommunication and econophysics. For complex matrices an explicit expression for the joint…
In this paper we study the volatility and its probability distribution function for the cumulative production based on the experience curve hypothesis. This work presents a generalization of the study of volatility in [1], which addressed…
A formalism is presented to obtain closed evolution equations for asymptotic probability distribution functions of turbulence magnitudes. The formalism is derived for a generic evolution equation, so that the final result can be easily…
This thesis reviews recent progress on products of random matrices from the perspective of exactly solved Gaussian random matrix models. We derive exact formulae for the correlation functions for the eigen- and singular values at arbitrary…
We introduce a sharpness functional for probabilistic models that quantifies sharpness as an intrinsic property of the probability distribution. The measure is derived based on a rank-based concentration principle that tracks upward…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
In this paper, we study the asymptotic behaviour of the product tail probability $ \mathbb{P}(\xi_1\cdots\xi_N \geqslant n), $ where $\{\xi_1,\ldots,\xi_N\}$ is a finite collection of independent Poisson random variables with positive…