Exact and Limiting Probability Distributions of Some Smirnov Type Statistics
- 1 February 1965
- journal article
- Published by Canadian Mathematical Society in Canadian Mathematical Bulletin
- Vol. 8 (1) , 93-103
- https://doi.org/10.4153/cmb-1965-012-5
Abstract
Let F(x) be the continuous distribution function of a random variable X and Fn(x) be the empirical distribution function determined by a random sample X1, …, Xn taken on X. Using the method of Birnbaum and Tingey [1] we are going to derive the exact distributions of the random variables and and where the indicated sup' s are taken over all x' s such that -∞ < x < xb and xa ≤ x < + ∞ with F(xb) = b, F(xa) = a in the first two cases and over all x' s so that Fn(x) ≤ b and a ≤ Fn(x) in the last two cases.Keywords
This publication has 2 references indexed in Scilit:
- One-Sided Confidence Contours for Probability Distribution FunctionsThe Annals of Mathematical Statistics, 1951
- On the Kolmogorov-Smirnov Limit Theorems for Empirical DistributionsThe Annals of Mathematical Statistics, 1948