Probability distribution of distances between local extrema of random number series

Details Probability distribution of distances between local extrema of random number series Probability distribution of distances between local extrema of random number series

2006-11-06

arxiv.org/abs/math/0611130v4

Mathematics

Statistics Theory

8 pages, 1 figure, 2 tables. This version updates a reference to an earlier work by Oshanin, and corrects a typo in equation 3

Scientific paper

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.

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