On the normal approximation of a negative binomial random sum

Autor:	Jonas Kazys Sunklodas
Rok vydání:	2015
Předmět:	Combinatorics Independent and identically distributed random variables Discrete mathematics Binomial approximation General Mathematics Sum of normally distributed random variables Negative binomial distribution Order (group theory) Stein's method Random variable Central limit theorem Mathematics
Zdroj:	Lithuanian Mathematical Journal. 55:150-158
ISSN:	1573-8825 0363-1672
DOI:	10.1007/s10986-015-9271-2
Popis:	We present upper bounds of the L s norms of the normal approximation for random sums of independent identically distributed random variables X 1 ,X 2 , . . . with zero means and finite absolute moments of order 2 + δ, 0 < δ ≤ 1, where the number of summands N is a negative binomial random variable with parameters r = 1, 2, . . . and 0 < p < 1, independent of the summands X 1 ,X 2 , . . . . The upper bounds obtained are of order r −δ/2 for all 1 ≤ s ≤ ∞. MSC: 60F05
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::20af395fb8f38093de4a5ce70d6d8e67 https://doi.org/10.1007/s10986-015-9271-2 Zobrazit plný text záznamu Full text from SpringerLink