Simplified plotting of statistical observations

18 August 1945

journal article
Published by American Geophysical Union (AGU) in EOS, Transactions American Geophysical Union

Vol. 26 (1) , 69-82
https://doi.org/10.1029/tr026i001p00069

Abstract

We consider the largest observation in a sample of size n and ask: What is the mean number of observations such that this value, or a larger one, happens once again? This question is important for statistical variates as earthquake magnitudes, precipitations, floods, temperatures, and pressures, where the largest value involves specific dangers. Similar problems arise in quality‐control and in gunnery.It will be shown that the mean number depends, in general, upon the nature of the variate. However, for a wide class of statistical distributions, it converges toward the sample‐size. The general solution given in the first section will be applied, in the second section, to some interesting distributions; in the last section it will be used to simplify the plotting procedure advocated in a previous article [see 6 of “References” at end of paper].

Keywords

This publication has 4 references indexed in Scilit:

On the plotting of flood‐discharges
EOS, Transactions American Geophysical Union, 1943
The Return Period of Flood Flows
The Annals of Mathematical Statistics, 1941
Limiting forms of the frequency distribution of the largest or smallest member of a sample
Mathematical Proceedings of the Cambridge Philosophical Society, 1928
ON THE EXTREME INDIVIDUALS AND THE RANGE OF SAMPLES TAKEN FROM A NORMAL POPULATION
Biometrika, 1925