Benford's law for exponential random variables
β Scribed by Hans-Andreas Engel; Christoph Leuenberger
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 192 KB
- Volume
- 63
- Category
- Article
- ISSN
- 0167-7152
No coin nor oath required. For personal study only.
β¦ Synopsis
Benford's law assigns the probability log 10 (1 + 1=d) for ΓΏnding a number starting with speciΓΏc signiΓΏcant digit d. We show that exponentially distributed numbers obey this law approximatively, i.e., within bounds of 0.03.
π SIMILAR VOLUMES
Under mild conditions, a Bernstein-Hoe ding-type inequality is established for covariance invariant positively associated random variables. A condition is given for almost sure convergence, and the associated rate of convergence is speciΓΏed in terms of the underlying covariance function.
Using the compactness in large deviation theory, this note describes a large deviation upper bound by a lower semicontinuous function. It then obtains a characterization for exponential convergence and discusses exponential convergence rates.
We obtain some new results on normalized spacings of independent exponential random variables with possibly different scale parameters. It is shown that the density functions of the individual normalized spacings in this case are mixtures of exponential distributions and, as a result, they are log-c