Limit distribution of a roundoff error
Copyright policy )Limit distribution of a roundoff error
Denote by \([x]:=\sup\{m\in\mathbb{Z}:\,m\leq x\}\) the integral part of \(x\in\mathbb{R}\) and by \(\{x\}:=x-[x]\in[0,1)\) its fractional part. Let \(X\) be a random variable. The conditional distribution function \(F_n(x):=P(\{X\}\leq x \mid [X]=n)\) for an integer \(n\in\mathbb{N}\) is investigated. Characterizations of the limit of \(F_n\) when \(n\) tends to infinity are established. The results cover most well-known continuous distribution functions.
fractional part of random variables60E05 65G50, Roundoff error, Asymptotic distribution theory in statistics, Characterization and structure theory of statistical distributions, Probability distributions: general theory, tail probabilitys
fractional part of random variables60E05 65G50, Roundoff error, Asymptotic distribution theory in statistics, Characterization and structure theory of statistical distributions, Probability distributions: general theory, tail probabilitys
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