Probability distribution of distances between local extrema of random number series
| dc.creator | Kuketayev, Argyn | |
| dc.date | 2006-11-06 | |
| dc.date | 2007-02-08 | |
| dc.date.accessioned | 2026-07-07T08:08:18Z | |
| dc.date.available | 2026-07-07T08:08:18Z | |
| dc.description | There is a sequence of random numbers x1,x2, ..., xn and so on. Numbers are independent of each other, but all numbers are from the same continuous distribution. If x1 < x2 > x3, then x2 is a local maximum. Here, we show that the probability mass function (PMF) of idstribution of distances between local maxima is non-parametric and the same for any probability distribution of random numbers in the sequence, and that the average distance is exactly 3. We present a method of computation of this PMF and its table for distances betwen 2 and 29. This PMF is confirmed to match distance distributions of sample random number sequences, which were created by pseudo-random number generators or obtained from "true" random number sources. | |
| dc.description | 8 pages, 1 figure, 2 tables. This version updates a reference to an earlier work by Oshanin, and corrects a typo in equation 3.1 (thanks to Eduardo D. da Costa for noticing it) | |
| dc.identifier | https://arxiv.org/abs/math/0611130 | |
| dc.identifier | http://arxiv.org/abs/math/0611130 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131221 | |
| dc.subject | Statistics Theory | |
| dc.subject | Probability | |
| dc.subject | 60G70 | |
| dc.title | Probability distribution of distances between local extrema of random number series | |
| dc.type | text |