An Introduction to the theory of statistics

Bibliographic data

Monograph

Identifikator:: 1751730271

URN:: urn:nbn:de:zbw-retromon-127610

Document type:: Monograph

Author:: Yule, George Udny http://d-nb.info/gnd/12910504X

Title:: An Introduction to the theory of statistics

Edition:: 8. ed. rev

Place of publication:: London

Publisher:: Griffin

Year of publication:: 1927

Scope:: XV, 422 S; Ill., Diagr

Digitisation:: 2021

Collection:: Economics Books

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SUPPLEMENTS—THE LAW OF SMALL CHANCES. 729 The frequent rediscovery of this theorem is due to the fact that its value is felt in the study of problems involving small, inde- pendent probabilities. For instance, if we desired to find the distribution of = things in IV pigeon-holes (all the pigeon-holes being of equal size and equally accessible), I being large, the dis- tribution given by the binomial 1, ¥-1} 7+) FTF would be effectively represented by (8), tables of which for different values of A have been published by v. Bortkewitsch and others. The theorem has also been applied to cases in which, although the actual value of ¢ (or p) is unknown, it may safely be assumed to be very small. It should be noticed that, if (8) is the real law of distribution, certain relations must obtain between the con- stants of the statistics (see par. 12, Chapter XIIL). Using the method of par. 6, Chapter XV., we have for the mean 23 eM A +A+ 2 pF ed 2! 2 : =re A(1+A+ 2+ eta ud 21 =A and for o? 3 eA(A+200 +30 ‘on ) - AZ . AZ A A 222 3A g =e SYRER EL. LY pe (A +2020 ceee)=A 2 =A+e-M(1 Xe 2 piri x 2! =A+A2-A2 = A. Hence any statistics produced by causes conforming to Poisson’s limit should, within the limits of sampling, have the mean equal to the square of the standard deviation. For instance, in the statistics used in par. 12 of Chapter XIII, the mean is ‘61, a="78, ¢2="6079, 2% 24

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