Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1154815 | Statistics & Probability Letters | 2012 | 7 Pages |
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
Authors
Takaaki Shimura,