Approximated maximum likelihood estimation of parameters of discrete stable family

Slámová, Lenka, and Klebanov, Lev B.. "Approximated maximum likelihood estimation of parameters of discrete stable family." Kybernetika 50.6 (2014): 1065-1076. <http://eudml.org/doc/262203>.

@article{Slámová2014,
abstract = {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 likelihood and other approach has to be applied. We depart from the $\mathcal \{H\}$-method of maximum likelihood suggested by Kagan (1976) where the likelihood function is replaced by a function called informant which is an approximation of the likelihood function in some Hilbert space. For this method only some functionals of the distribution are required, such as probability generating function or characteristic function. We adopt this method for the case of discrete stable distributions and in a simulation study show the performance of this method.},
author = {Slámová, Lenka, Klebanov, Lev B.},
journal = {Kybernetika},
keywords = {discrete stable distribution; parameter estimation; maximum likelihood; discrete stable distribution; parameter estimation; maximum likelihood},
language = {eng},
number = {6},
pages = {1065-1076},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Approximated maximum likelihood estimation of parameters of discrete stable family},
url = {http://eudml.org/doc/262203},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Slámová, Lenka
AU - Klebanov, Lev B.
TI - Approximated maximum likelihood estimation of parameters of discrete stable family
JO - Kybernetika
PY - 2014
PB - Institute of Information Theory and Automation AS CR
VL - 50
IS - 6
SP - 1065
EP - 1076
AB - 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 likelihood and other approach has to be applied. We depart from the $\mathcal {H}$-method of maximum likelihood suggested by Kagan (1976) where the likelihood function is replaced by a function called informant which is an approximation of the likelihood function in some Hilbert space. For this method only some functionals of the distribution are required, such as probability generating function or characteristic function. We adopt this method for the case of discrete stable distributions and in a simulation study show the performance of this method.
LA - eng
KW - discrete stable distribution; parameter estimation; maximum likelihood; discrete stable distribution; parameter estimation; maximum likelihood
UR - http://eudml.org/doc/262203
ER -