ON NUMBER OF UNOBSERVED POSITIVE INTEGERS LESS THAN THE MAXIMUM SAMPLE FROM GEM DISTRIBUTION - Collections

＜journal article＞
ON NUMBER OF UNOBSERVED POSITIVE INTEGERS LESS THAN THE MAXIMUM SAMPLE FROM GEM DISTRIBUTION

Creator	Author PID 90041227 Creator Name Yamato, Hajime 大和, 元ヤマト, ハジメ Affiliation Affiliation Name Emeritus of Kagoshima University 鹿児島大学 : 名誉教授
Language	English
Publisher	Research Association of Statistical Sciences
Publisher	統計科学研究会
Date	2022
Source Title	Bulletin of informatics and cybernetics
Vol	54
Issue	5
First Page	1
Last Page	13
Publication Type	Version of Record
Access Rights	open access
Crossref DOI	https://doi.org/10.5109/4844361
Abstract	For a sample from GEM distribution considered as a random discrete distribution of positive integers, there are probably unobserved less positive integers than the maximum sample. The number of these ...integers follows a mixed Poisson distribution. Here, we provide a simple proof of the convergence in distribution of this number. Similarly, its asymptotic distribution is a mixed Poisson. We derived the upper bounds for the total variation between the finite and asymptotic distributions. These distributions are illustrated by examples; the related total values are provided in table 1.show more

File	FileType	Size	Views	Description
BIC-54-5	pdf	333 KB	138

PISSN	0286-522X
EISSN	2435-743X
NCID	AA10634475
Record ID	4844361
Peer-Reviewed	Refereed
Subject Terms	convergence in distribution
	GEM distribution
	mixed Poisson distribution
	mixing distribution
	number of unobserved positive integers
	order statistics
	total variation distance
Created Date	2022.10.24
Modified Date	2022.10.24