Tables of Critical Values of Some Rényi Type Statistics for Finite Sample Sizes

Abstract

Let X₍₁₎ ≤ X ₍₂₎ ≤ … ≤ X _(n) be an ordered sample of a random variable X which has continuous probability distribution function F (x), and let F_n (x) be the corresponding empirical distribution function. The following three statistics, introduced by A. Rényi, are considered:

The paper presents table of exact probabilities for these statistics for finite sample sizes. The limiting distributions of these statistics for sample size n ∞ are discussed, and sample sizes are indicated for which these limiting distributions can be used instead of the exact distributions. Numerical examples for the use of the tables are presented, as well as applications to testing hypotheses on life distributions and to one-sided estimation of probability distribution functions from censored data.