On the Poisson-Type Arrival of Order Statistics

• Activity Number: 21
• Type: Topic Contributed
• Date/Time: Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Karthik Bharath*+ and Haikady Nagaraja
• Companies: Ohio State University and The Ohio State University
• Keywords: Spacings ; Regular Variation ; von Mises conditions ; Poisson process

Abstract

We demonstrate that the result regarding convergence to a unit-mean exponential r.v of uniform spacings scaled by the sample size, can be extended to general spacings induced by random variables with arbitrary continuous distribution under appropriate normalization which depends intricately on the quantile function. Using the result we then construct a counting process on the counts of order statistics (central, intermediate and extreme) and establish the sufficient conditions under which the counting process converges weakly to a homogeneous Poisson process with unit intensity; this then generalizes existing results regarding Poisson-distributed counts in the neighborhood of an order statistic