``Weather'' Records: Musings on Cold Days after a Long Hot Indian Summer

TL;DR

This paper introduces the statistics of extreme values through a simple model inspired by record high temperatures, revealing universal properties of record lifetimes and distributions independent of the underlying data distribution.

Contribution

It provides a pedagogical and simplified model demonstrating universal statistical behaviors of records in sequences of independent, identically distributed random variables.

Findings

Record lifetime histogram is universal across distributions.

Distribution and averages of record values are derived.

Universal properties hold regardless of the underlying distribution.

Abstract

We present a simple, pedagogical introduction to the statistics of extreme values. Motivated by a string of record high temperatures in December 1998, we consider the distribution, averages and lifetimes for a simplified model of such ``records.'' Our ``data'' are sequences of independent random numbers all of which are generated from the same probability distribution. A remarkable universality emerges: a number of results, including the lifetime histogram, are universal, that is, independent of the underlying distribution.