Probability distribution of distances between local extrema of random number series

Abstract

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.