Accession Number : AD0643955

Title :   APPROXIMATING THE BINOMIAL, F, AND COMMONLY USED RELATED DISTRIBUTIONS, II.

Descriptive Note : Technical rept.,

Corporate Author : HARVARD UNIV CAMBRIDGE MASS DEPT OF STATISTICS

Personal Author(s) : Pratt,John W.

Report Date : AUG 1966

Pagination or Media Count : 54

Abstract : The paper describes and derives the asymptotic behavior of the new Normal approximation introduced in Part I (AD-943 954) and of a family of Normal approximations based on roots, including the square root approximations of Fisher, and Freeman and Tukey, and the cube root approximations of Wilson and Hilferty, Camp, and Paulson. Various asymptotic comparisons are made, all of which rank the new approximation first, the cube root approximations second, and the other root approximations (and the ordinary Normal approximation) third. For instance, in the binomial case, if the tail probability is fixed as n approaches limit of infinity, the errors resulting from the foregoing approximations are generally of order n to the minus 3/2 power, /n, and n to the minus 1/2 power respectively, while for a tail probability approaching 0 the relative error in approximating it approaches 0, if the corresponding standard Normal deviate is of smaller order than n to the 1/2 power, n to the 1/4 power, of n to the 1/6 power respectively, but not generally otherwise. These comparisons are deduced from far more detailed results which are also given. (Author)

Descriptors :   (*STATISTICAL DISTRIBUTIONS, *APPROXIMATION(MATHEMATICS)), MATHEMATICAL LOGIC, BINOMIALS, FUNCTIONAL ANALYSIS, TABLES(DATA)

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE