Asymptotically Independent Scale-Free Spacings with Applications to Discordancy Testing

Abstract

Motivated by the construction of independent scale-free spacings for the exponential distribution, analogous quantities are defined for an arbitrary distribution, and their joint asymptotic behaviour studied under suitable tail conditions. These scale-free spacings provide a unified approach to the problem of consecutive discordancy testing when location and scale parameters are unknown. A normal example is discussed and the accuracy of the approximations assessed via some Monte Carlo studies.