On One Identity for Distribution of Sums of Independent Random Variables
| Autor: | V. M. Kruglov |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Statistics and Probability
Exchangeable random variables Combinatorics Pairwise independence Independent and identically distributed random variables Discrete mathematics Indecomposable distribution Sum of normally distributed random variables Illustration of the central limit theorem Statistics Probability and Uncertainty Marginal distribution Central limit theorem Mathematics |
| Zdroj: | Theory of Probability & Its Applications. 58:329-331 |
| ISSN: | 1095-7219 0040-585X |
| DOI: | 10.1137/s0040585x97986576 |
| Popis: | In a 1957 paper F. Spitzer published, among other things, one estimate of the distribution function of sums of independent symmetric random variables with a common absolutely continuous distribution. This estimation was constructed with the help of one identity for the distribution of a sum of the above-mentioned random variables, the proof of which was not given. In this paper we prove the Spitzer identity for any independent random variables, and by using it we construct an estimate of the distribution of a sum of independent identically distributed random variables. The Spitzer estimate can be derived as a particular case of the proposed estimation. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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