Local limit approximations for Lagrangian distributions
type: Item
instance of: scholarly article
title: Local limit approximations for Lagrangian distributions
zbMATH Open document ID: 0815.60019
DOI: 10.1007/BF01827929
published in: Aequationes Mathematicae
publication date: 1995-06-30T00:00:00Z
full work available at URL: https://eudml.org/doc/182472
review text: The Lagrange distribution, given by \[ P(0) = 0, \quad P(m) = {1\over m!} {d^{m - 1}\over dz^{m - 1}} (f'(z) g^ m(z)),\quad \quad z = 0,\;m = 1,2,\dots, \] with probability generating functions \(f\), \(g\), \(g(0)= 0\), studied for the case that \[ f(z) = \varphi(\lambda z)/\varphi(\lambda),\quad\quad g(z) = \psi(\mu z)/\psi(\mu), \] where \(\varphi\), \(\psi\) are power series with non-negative coefficients. Under suitable assumptions on \(\varphi\), \(\psi\), local limit theorems are derived for \(m \to \infty\) with \(\lambda\), \(\mu\) changing appropriately. These results lead to approximations for well-known special distributions of Lagrangian type.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60E10
Mathematics Subject Classification ID: 05A16
Mathematics Subject Classification ID: 60C05
zbMATH DE Number: 729146
zbMATH Keywords: approximation of distributions
zbMATH Keywords: Lagrange distribution
zbMATH Keywords: probability generating functions
zbMATH Keywords: local limit theorems
author: Ljuben Mutafchiev
reviewed by: Heinrich Hering
MaRDI profile type: Publication
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OpenAlex ID: W2087794744
description: scientific article; zbMATH DE number 729146