Image: KolmogorovDistrPDF

Description: Kolmogorov Distribution PDF. Here is the R code used to generate it: res = 1e-3 xmax = 3 jmax = 1e4 js = 1 : jmax xs = seq(from = 0, to = xmax, by = res) Fx = array(NA, length(xs)) sqrt_two_pi = sqrt(2 * pi) for (i in 1 : length(xs)){ x = xs[i] Fx[i] = sqrt_two_pi / x * sum(exp(-(2 * js - 1)^2 * pi^2 / (8 * x^2))) if (i %% 100 == 0){ cat("F(", x, ") =", Fx[i], "\n") } } pacman::p_load(ggplot2) fx = array(NA, length(xs)) for (i in 1 : (length(xs) - 1)){ fx[i] = (Fx[i + 1] - Fx[i]) / res } ggplot(data.frame(xs = xs, fx = fx, Fx = Fx)) + geom_line(aes(x = xs, y = fx)) + xlab("k") + ylab("f_K(k)")
Title: KolmogorovDistrPDF
Credit: Own work
Author: Adam Kapelner, PhD
Usage Terms: Creative Commons Attribution-Share Alike 4.0
License: CC BY-SA 4.0
License Link: https://creativecommons.org/licenses/by-sa/4.0
Attribution Required?: Yes