The Variance of the Discrepancy Distribution of Rounding Procedures, and Sums of Uniform Random Variables
- When l probabilities are rounded to integer multiples of a given accuracy n, the sum of the numerators may deviate from n by a nonzero discrepancy. It is proved that, for large accuracies n --> infinty, the limiting discrepancy distribution has variance l/12. The relation to the uniform distribution over the interval [-1/2, 1/2], whose variance is 1/12, is explored in detail.
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| Author: | Lothar HeinrichGND, Friedrich PukelsheimGND, Vitali WachtelGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-37675 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/3767 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2016-02) |
| Type: | Preprint |
| Language: | English |
| Date of Publication (online): | 2016/06/08 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2016/06/08 |
| Tag: | Euler-Frobenius polynomial; Euler-Maclaurin formula; Fourier-analytic approach; rounding residual |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Stochastik und ihre Anwendungen | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  Deutsches Urheberrecht |
