Products of random variables and the first digit phenomenon
| Autor: | Nicolas Chenavier, Dominique Schneider, Bruno Massé |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Statistics and Probability
Discrete mathematics Sequence Statistics::Theory Distribution (number theory) Weak convergence Applied Mathematics Modulo 010102 general mathematics Mathematics::History and Overview Probability (math.PR) 01 natural sciences Benford's law 010104 statistics & probability Significand Mathematics::Probability Modeling and Simulation FOS: Mathematics Almost surely 0101 mathematics Random variable Mathematics - Probability Mathematics |
| DOI: | 10.48550/arxiv.1512.06049 |
| Popis: | We provide conditions on dependent and on non-stationary random variables X n ensuring that the mantissa of the sequence of products ∏ 1 n X k is almost surely distributed following Benford’s law or converges in distribution to Benford’s law. This is achieved through proving new generalizations of Levy’s and Robbins’s results on distribution modulo 1 of sums of independent random variables. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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