The program display the optimized values of binomial distribution 95% confidence intervals for proportion from n = 2 to n = 534 computed using a completely new and original algorithm.
Usage (for n = 20, X = 5): /applied_statistics/binomial_distribution/?n=20
Or: /applied_statistics/binomial_distribution/?n=20&X=5
References for behaviour of other CI calculation methods:
Binomial Distribution Sample Confidence Intervals Estimation 1. Sampling and Medical Key Parameters Calculation, Tudor DRUGAN, Sorana BOLBOACĂ, Lorentz JÄNTSCHI, Andrei ACHIMAS CADARIU, http://lejpt.academicdirect.org/A03.
Binomial Distribution Sample Confidence Intervals Estimation 2. Proportion-like Medical Key Parameters, Sorana BOLBOACĂ, Andrei ACHIMAS CADARIU, http://lejpt.academicdirect.org/A03.

& Sorana BOLBOACĂ

	ci			er
0.0							0%
0.5							5%
1.0							10%
	0.0	0.5	1.0	0	10	20

n	X	_95%ci_L	_95%ci_U	er
20	0	0.000	0.147	0.000
20	1	0.003	0.247	7.548
20	2	0.003	0.297	4.317
20	3	0.053	0.397	6.069
20	4	0.053	0.448	4.367
20	5	0.102	0.497	6.524
20	6	0.102	0.547	5.263
20	7	0.152	0.597	3.170
20	8	0.202	0.647	3.699
20	9	0.253	0.698	4.028
20	10	0.253	0.748	4.139
20	11	0.302	0.748	4.028
20	12	0.352	0.797	3.699
20	13	0.403	0.848	3.170
20	14	0.453	0.897	5.263
20	15	0.503	0.897	6.524
20	16	0.552	0.948	4.367
20	17	0.603	0.948	6.069
20	18	0.703	0.998	4.317
20	19	0.753	0.998	7.548
20	20	0.853	1.000	0.000