Limit distribution of a roundoff error

Takaaki Shimura

Statistics & Probability Letters, 2012, vol. 82, issue 4, 713-719

Abstract: 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.

Keywords: Roundoff error; Tail probability; Hazard function; Distribution of fractional part of a random variable (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715211004135
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:82:y:2012:i:4:p:713-719

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2011.12.021

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().