APPROXIMATING THE BINOMIAL, F, AND COMMONLY USED RELATED DISTRIBUTIONS, I.
Abstract
The paper concerns a new Normal approximation to the beta distribution and its relatives, in particular, the binomial, Pascal negative binomial, F, t, Poisson, gamma, and chi square distributions. The approximate Normal deviates are expressible in terms of algebraic functions and logarithms, but for desk calculation it is preferable to use an equivalent expression in terms of a function specially tabulated here. The t distribution and its relatives are handled by a special method, for which further tables are given. Graphs of the error are provided. They show that the approximation is good even in the extreme tails except for beta distributions which are J or U shaped or nearly so, and they permit correction to obtain still more accuracy. Further graphs compare various Normal approximations. Some classical continued fractions and some standard recursive relations which may occasionally be useful are also given. Everything an ordinary user of the approximation might want to know is included in this paper. The theory behind the approximation and most proofs are postponed to a second paper immediately following this one (AD-643 955). (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1966
- Accession Number
- AD0643954
Entities
People
- David B. Peizer
- John W. Pratt
Organizations
- Harvard University