Almost sure limit behaviour of Pfeifer record values

Statistics, vol. 54, pp. 830–840

Abstract

Pfeifer record values are based on a double sequence of independent, non-identically distributed random variables. For Pfeifer records with a common baseline distribution function and depending on a sequence of positive parameters, almost sure convergence to a non-degenerate random variable is examined, and sufficient conditions for almost sure relative stability as well as related results are studied. Several examples of sequences of model parameters are shown regarding the imposed conditions. The results extend well-known properties of common upper record values.

Authors 2

1. Jacob Peter Schmidt Aachen Institute of Statistics

   RWTH Aachen University

   Affiliation as printed

   Institute of Statistics, RWTH Aachen University, Aachen, Germany

2. Udo Kamps corresponding Aachen Institute of Statistics

   RWTH Aachen University

   Affiliation as printed

   Institute of Statistics, RWTH Aachen University, Aachen, Germany