TOW PROBABILITY LIMIT THEOREMS AND AN APPLICATION,

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Abstract:

A necessary and sufficient condition that the limit distribution of a log-normal random variable be normal as the mean becomes large is presented. A similar result for the non-central chi-square random variable is also included. A set of sufficient conditions, following some recent work of Trotters, is given for the limit normality, without assuming moments, for a class of distributions depending on a continuous parameter that tends to infinity. Application of these results to some .ansformations in the analysis of variance when the mean values are large is indicated. Author

Author(s):
Rao, M. M.
Author Organization(s):
CARNEGIE INST OF TECH PITTSBURGH PA
Supplementary Note:
Pub. in Akademie van Wetenschappen, Amsterdam. Proceedings, series A v64 n5 and Indag. Math. v23 n5 p552-9 1961 (Copies available only to DDC users).
Annotation:
Reprint: Two probability limit theorems and an application.
Pagination:
0009

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:
Approved For Public Release

RECORD

Collection: TR
Identifying Numbers
Contract/Grant Number(s):
AF 33(616)-3878, NSF-G14832
 Subject Terms
Communities of Interest:
No COI(s) Identified
Descriptor(s):
(*DISTRIBUTION THEORY, PROBABILITY), (*PROBABILITY, DISTRIBUTION THEORY), TRANSFORMATIONS(MATHEMATICS), ANALYSIS OF VARIANCE, STOCHASTIC PROCESSES, THEOREMS
Keyword(s):
LIMIT THEOREMS
Report Date:
1960 Jan 01