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CRITICAL VALUES FOR INFERENCE ABOUT NORMAL DISPERSION 1
Author(s) -
John S.
Publication year - 1973
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1973.tb00010.x
Subject(s) - mathematics , decimal , table (database) , combinatorics , poisson distribution , simple (philosophy) , arithmetic , statistics , function (biology) , computer science , philosophy , epistemology , evolutionary biology , biology , data mining
Summary Let F N (.) be the density function of X 2 N . Values of C 1 /N, i = 1, 2, satisfying the twin conditions Pr (C 1 ≤X 2 N ≤C 2 ) =1‐α and the conditional expectation of X 2 N given C 1 ≤X 2 N ≤C 2 is N are tabulated for α=.2, .1, .05, .01, .005, .001, N =1(1)20(2)50(5)150(10)350. The second condition may be replaced by the condition f N+2 (C 1 )=f N+2V (C 2 ). The author has with him a bigger table giving C 1 and C 2 for α=.2, .1, .05, .01, .005, .001, N=1(1)350 to three decimals (to three significant digits, if some decimals are not significant). Several applications are mentioned. A practical application that is perhaps not obvious is to test whether two or more counts are distributed as independent Poisson variables. The new simple formulae used in the construction of the table are given and should prove useful in obtaining accurate values for omitted entries and in increasing the accuracy of entries.