Random record models

Abstract

We study record times, mainly, and sizes in the following context. Let Xn denote the size of the nth event occurring in a point stochastic pacing process 𝒫. The Xn is i.i.d. and 𝒫 is, variously, Poisson, negative binomial, renewal and Furry. Explicit distributions of first-record times are found, domains of attraction studied and the asymptotic lognormality of the nth-record time is shown for Poisson 𝒫.