The Bell System technical journal (1922) (14569415218)

Identifier: b00ellsystemtechniamervol5rich (find matches)

Title: The Bell System technical journal

Year: 1922 (1920s)

Authors: American Telephone and Telegraph Company

Subjects: Telecommunication Electric engineering Communication Electronics Science Technology

Publisher: (Short Hills, N.J., etc., American Telephone and Telegraph Co.)

Contributing Library: Prelinger Library

Digitizing Sponsor: Internet Archive

Text Appearing Before Image:

served distributions shownhere have been represented, as in Fig. 4, with the vertical line rep- A more detailed discussion of the effect of finite sampling will be found in thepaper by G. A. Campbell previously referred to. * See Explanation of Deviations from Poissons Law in Practice, by Student,Biometrika, Vol. 12, pp. 211-215, 1919. IT ION 613 tion terminated atpoints in the rangedots and the pointscenters. This sec-•ase in reliabiHty ofd is gradual. There■ven in the center as ■ introduce a definiteIt to the right suchwhen the value of a7 shows three theo-^ame average a = 75.g a = 50 and a = 100,ratio of 3 :1, havingial sub-series havingshows the effect oni uniformly betweende up of two equalvn for comparison.r decreases with theto occur frequently,imaterial whether ads in the sample, ornts happening at aoughout the series a■ies the tendency tolevices may be em-ual series, some ofbelow. on summation onlybe some reason to .999- .9399- Pi = P(c,a,). .99999-^- .999999 a • 0,

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Fig. 5—Probability curves showing Poissons exponential summation for the probability P that an event occur at least c times in a large group of trials for which the average number of occurrences is a. A scale proportional to the normal probability integral is used for P, a logarithmic scale for a POISSONS PROBABILITY SUMMATION 613 resenting the corresponding l\)isson distribution terminated atP = l A and P=l — 1N, and with the observed points in the rangeP=10 N to P=l—10N shown as soHd black dots and the pointsoutside this range shown as circles with white centers. This sec-ondar\- division is quite arbitrary, for the increase in relial)ility ofthe points as the center of the range is approached is gradual. Therewill, of course, be irregularities due to sampling even in the center aslong as the number of samples is finite. Non-uniforniit\- of the samples of the series may introduce a definitetrend away from the Poisson distribution, a slant to the right suchas is shown in Figs.

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1922

Prelinger Library

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