๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

On the Asymptotic Logarithmic Distribution of the Floating-Point Mantissas of Sums

โœ Scribed by Peter Schatte


Publisher
John Wiley and Sons
Year
1986
Tongue
English
Weight
479 KB
Volume
125
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

โœฆ Synopsis


Proof. If the Xi are replaced by -Xi, the hn(r) do not be changed. Therefore we can assume a>O. Let H,(z) be the distribution function of the random


๐Ÿ“œ SIMILAR VOLUMES


On the Almost Sure Convergence of Floati
โœ Peter Schatte ๐Ÿ“‚ Article ๐Ÿ“… 1988 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 238 KB ๐Ÿ‘ 1 views

Let Y1, Y2, ... be a sequence of random variables 8nd let J i n be the floating-point mantissa of Y,,. Further let l f ~, ~) ( , ) denote the indicator function of the interval [I, x). If Yn/n-Z as.. wheteZ+O is 5 fnrther random variable, then the seqirence i~~,z#3fn) converges a s . to log x in the

Asymptotic Distribution of the Distance
โœ Pavel Kargaev; Anatoly Zhigljavsky ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 337 KB

Let x be a real number in [0, 1], F n be the Farey sequence of order n and \ n (x) be the distance between x and F n . Assuming that n ร„ we derive the asymptotic distributions of the functions n 2 \ n (x) and n\ n (x$ร‚n), 0 x$ n. We also establish the asymptotics for 1 0 \ $ n (x) dx, for all real $