Tests of significance in harmonic analysis

A - Papers appearing in refereed journals

Fisher, R. A. 1929. Tests of significance in harmonic analysis. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 125 (796), pp. 54-59. https://doi.org/10.1098/rspa.1929.0151

AuthorsFisher, R. A.
Abstract

If a series u1, u2,...u2n + 1 constitute a random sample from a normally distributed population, they any linear function A = S 1 2n + 1 (arur) will also be normally distributed; moreover its mean will be zero if S(ar) = 0, and its variance will be equal to that of the original population if S (ar2) = 1. Any other liner function B = S 1 2n + 1 (brur) will be distributed independently of the first if S(arbr) = 0, and in this case the sum of the squares, x = A2 + B2, will be distributed so that the chance of exceeding any particular value of x is e -x/e, where c is the mean value of x, equal to twice the variance of the population sampled.

Year of Publication1929
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Journal citation125 (796), pp. 54-59
Digital Object Identifier (DOI)https://doi.org/10.1098/rspa.1929.0151
Open accessPublished as non-open access
PublisherRoyal Society Publishing
ISSN1364-5021

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