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Approximated maximum likelihood estimation of parameters of discrete stable family

Lenka Slámová, Lev B. Klebanov (2014)

Kybernetika

In this article we propose a method of parameters estimation for the class of discrete stable laws. Discrete stable distributions form a discrete analogy to classical stable distributions and share many interesting properties with them such as heavy tails and skewness. Similarly as stable laws discrete stable distributions are defined through characteristic function and do not posses a probability mass function in closed form. This inhibits the use of classical estimation methods such as maximum...

Approximation by Poisson law

Aldona Aleškevičienė, Vytautas Statulevičius (2005)

Discussiones Mathematicae Probability and Statistics

We present here the results of the investigation on approximation by the Poisson law of distributions of sums of random variables in the scheme of series. We give the results pertaining to the behaviour of large deviation probabilities and asymptotic expansions, to the method of cumulants, with the aid of which our results have been obtained.

Approximation of a symmetric α-stable Lévy process by a Lévy process with finite moments of all orders

Z. Michna (2007)

Studia Mathematica

In this paper we consider a symmetric α-stable Lévy process Z. We use a series representation of Z to condition it on the largest jump. Under this condition, Z can be presented as a sum of two independent processes. One of them is a Lévy process Y x parametrized by x > 0 which has finite moments of all orders. We show that Y x converges to Z uniformly on compact sets with probability one as x↓ 0. The first term in the cumulant expansion of Y x corresponds to a Brownian motion which implies that Y x can...

Approximation of bivariate Markov chains by one-dimensional diffusion processes

Daniela Kuklíková (1978)

Aplikace matematiky

The paper deals with several questions of the diffusion approximation. The goal of this paper is to create the general method of reducting the dimension of the model with the aid of the diffusion approximation. Especially, two dimensional random variables are approximated by one-dimensional diffusion process by replacing one of its coordinates by a certain characteristic, e.g. by its stationary expectation. The suggested method is used for several different systems. For instance, the method is applicable...

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