Abstract
An analysis is made of the probability distribution of the largest values attained by a stationary random variable
f
(
t
) over a period of time containing several oscillations. Exact computations are made and asymptotic formulae are derived for the expectation and standard error of the first, second and third greatest maxima in terms of √
m
0
, the r. m. s. deviation of
f
(
t
) about its mean value, on the assumption that successive waves are uncorrelated; an analysis is also made of the corrections necessary to allow for mutual correlation when
f
(
t
) has a narrow spectrum. The results are applied to measurements from a 24 h record of ocean waves containing some 10000 oscillations.
Reference17 articles.
1. The statistical distribution of the maxima of a random function
2. Limiting forms of the frequency distribution of the largest or smallest member of a sample
3. Gumbel E. J. 1954 Statistical theory of extreme values and some practical applications. Appl. Math. Ser. 33 U.S. Bur. Stand.
4. Kendall M. G. 1945 The advanced theory of staol. 1 2nd ed. London: Griffin.
5. On the statistical distribution of the heights of sea waves;Longuet-Higgins M. S.;J. Mar. Res.,1952
Cited by
25 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献