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Sums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws

Klebanov, Lev;  Rachev, Svetlozar — 1996

Serdica Mathematical Journal

* Research supported by NATO GRANT CRG 900 798 and by Humboldt Award for U.S. Scientists. In this paper a general theory of a random number of random variables is constructed. A description of all random variables ν admitting an analog of the Gaussian distribution under ν-summation, that is, the summation of a random number ν of random terms, is given. The v-infinitely divisible distributions are described for these ν-summations and finite estimates of the approximation of ν-sum distributions...

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...

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