Article ID Journal Published Year Pages File Type
1154815 Statistics & Probability Letters 2012 7 Pages PDF
Abstract

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

Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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