On the Almost Sure Convergence of Floating‐Point Mantissas and Benford's Law | Zendy

Schatte Peter | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

On the Almost Sure Convergence of Floating‐Point Mantissas and Benford's Law

Author(s) -

Schatte Peter

Publication year - 1988

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.19881350108

Subject(s) - mathematics , benford's law , sequence (biology) , law of large numbers , random variable , logarithm , interval (graph theory) , combinatorics , convergence (economics) , discrete mathematics , statistics , mathematical analysis , genetics , economics , biology , economic growth

Let Y 1 , Y 2 ,… be a sequence of random variables and let M n be the floating‐point mantissa of Y n . Further let 1 1, x ) (·) denote the indicator of the interval (1, x ). If Y n / n → Z a.s., where Z ≠ 0 is a further random variable, then the sequence 1 (1, x ) ( M n ) converges a.s. to log x in the sense of ∞‐means and logarithmic means, respectively. The speed of convergence in this relations is estimated. As a conclusion, a further argument for Benford's law is provided.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research