Confidence limits for parameters of Poisson and binomial distributions
The confidence limits for the frequency in a Poisson process and for the proportion of successes in a binomial process were calculated and tabulated for the situations in which the observed values of the frequency or proportion and an a priori distribution of these parameters are available. Methods are used that produce limits with exactly the stated confidence levels. The confidence interval (a,b) is calculated so that Pr (a less than or equal to lambda less than or equal to b c,..mu..), where c is the observed value of the parameter, and ..mu.. is the a priori hypothesis of the distribution of this parameter. A Bayesian type analysis is used. The intervals calculated are narrower and appreciably different from results, known to be conservative, that are often used in problems of this type. Pearson and Hartley recognized the characteristics of their methods and contemplated that exact methods could someday be used. The calculation of the exact intervals requires involved numerical analyses readily implemented only on digital computers not available to Pearson and Hartley. A Monte Carlo experiment was conducted to verify a selected interval from those calculated. This numerical experiment confirmed the results of the analytical methods and the prediction of Pearson and Hartley that their published tables give conservative results.
- Research Organization:
- Du Pont de Nemours (E.I.) and Co., Aiken, SC (United States). Savannah River Lab.
- DOE Contract Number:
- AT(07-2)-1
- OSTI ID:
- 7361200
- Report Number(s):
- DP-1416; TRN: 76-018024
- Country of Publication:
- United States
- Language:
- English
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