Limit distribution of a roundoff error

Let [X] and {X} be the integer and the fractional parts of a random variable X. The conditional distribution function Fn(x)=P({X}≤x|[X]=n) for an integer n is investigated. Fn for a large n is regarded as the distribution of a roundoff error in an extremal event. For most well-known continuous distributions, it is shown that Fn converges as n→∞ and three types of limit distributions appear as the limit distribution according to the tail behavior of F.

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Year of publication:	2012
Authors:	Shimura, Takaaki
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 82.2012, 4, p. 713-719
Publisher:	Elsevier
Subject:	Roundoff error \| Tail probability \| Hazard function \| Distribution of fractional part of a random variable

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011040058