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A Normal Approximation for Binomial,F, Beta, and other Common, Related Tail Probabilities, I
- Source :
- Journal of the American Statistical Association. 63:1416-1456
- Publication Year :
- 1968
- Publisher :
- Informa UK Limited, 1968.
-
Abstract
- This 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 in most cases to use an equivalent expression in terms of a function specially tabulated here. 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. For use beyond the range of the graphs, some standard recursive relations and some classical continued fractions are listed, with some properties of the latter which seem to be partly new. Various Normal approximations are compared, with further graphs. The new approximation appears far more accurate than the others. Everything an ordinary user of th...
- Subjects :
- Statistics and Probability
Combinatorics
Binomial distribution
Beta negative binomial distribution
Binomial approximation
Negative binomial distribution
Central binomial coefficient
Statistics, Probability and Uncertainty
Binomial proportion confidence interval
Beta distribution
Binomial coefficient
Mathematics
Subjects
Details
- ISSN :
- 1537274X and 01621459
- Volume :
- 63
- Database :
- OpenAIRE
- Journal :
- Journal of the American Statistical Association
- Accession number :
- edsair.doi...........a5c25d52c4630a151ac7a4c8a1080d4b