ciEX: Exact method of CI estimation
In proportion: Inference on Single Binomial Proportion and Bayesian Computations

Description Usage Arguments Details Value References See Also Examples

Exact method of CI estimation

1	ciEX(n, alp, e)

`n`	- Number of trials
`alp`	- Alpha value (significance level required)
`e`	- Exact method indicator in [0, 1] 1: Clopper Pearson, 0.5: Mid P, The input can also be a range of values between 0 and 1.

Confidence interval for p (for all x = 0, 1, 2 ..n), based on inverting equal-tailed binomial tests with null hypothesis

H0: p = p0

and calculated from the cumulative binomial distribution. Exact two sided P-value is usually calculated as

P= 2[e*Pr(X = x) + min{(Pr(X < x), Pr(X > x))}]

where probabilities are found at null value of p and 0 <= e <= 1. The Confidence Interval of n given alp along with lower and upper abberation.

A dataframe with

`x`	- Number of successes (positive samples)
`LEX`	- Exact Lower limit
`UEX`	- Exact Upper Limit
`LABB`	- Likelihood Ratio Lower Abberation
`UABB`	- Likelihood Ratio Upper Abberation
`ZWI`	- Zero Width Interval
`e`	- Exact method input

[1] 1993 Vollset SE. Confidence intervals for a binomial proportion. Statistics in Medicine: 12; 809 - 824.

[2] 1998 Agresti A and Coull BA. Approximate is better than "Exact" for interval estimation of binomial proportions. The American Statistician: 52; 119 - 126.

[3] 1998 Newcombe RG. Two-sided confidence intervals for the single proportion: Comparison of seven methods. Statistics in Medicine: 17; 857 - 872.

[4] 2001 Brown LD, Cai TT and DasGupta A. Interval estimation for a binomial proportion. Statistical Science: 16; 101 - 133.

[5] 2002 Pan W. Approximate confidence intervals for one proportion and difference of two proportions Computational Statistics and Data Analysis 40, 128, 143-157.

[6] 2008 Pires, A.M., Amado, C. Interval Estimators for a Binomial Proportion: Comparison of Twenty Methods. REVSTAT - Statistical Journal, 6, 165-197.

[7] 2014 Martin Andres, A. and Alvarez Hernandez, M. Two-tailed asymptotic inferences for a proportion. Journal of Applied Statistics, 41, 7, 1516-1529

prop.test and binom.test for equivalent base Stats R functionality, binom.confint provides similar functionality for 11 methods, wald2ci which provides multiple functions for CI calculation , binom.blaker.limits which calculates Blaker CI which is not covered here and propCI which provides similar functionality.

Other Basic methods of CI estimation: PlotciAS, PlotciAllg, PlotciAll, PlotciBA, PlotciEX, PlotciLR, PlotciLT, PlotciSC, PlotciTW, PlotciWD, ciAS, ciAll, ciBA, ciLR, ciLT, ciSC, ciTW, ciWD

n=5; alp=0.05;e=0.5
ciEX(n,alp,e) #Mid-p
n=5; alp=0.05;e=1 #Clopper-Pearson
ciEX(n,alp,e)
n=5; alp=0.05;e=c(0.1,0.5,0.95,1) #Range including Mid-p and Clopper-Pearson
ciEX(n,alp,e)

  x        LEX       UEX LABB UABB ZWI   e
1 0 0.00000000 0.4507197   NO   NO  NO 0.5
2 1 0.01001220 0.6655550   NO   NO  NO 0.5
3 2 0.07347783 0.8176210   NO   NO  NO 0.5
4 3 0.18237899 0.9265222   NO   NO  NO 0.5
5 4 0.33444505 0.9899878   NO   NO  NO 0.5
6 5 0.54928027 1.0000000   NO   NO  NO 0.5
  x        LEX       UEX LABB UABB ZWI e
1 0 0.00000000 0.5218238   NO   NO  NO 1
2 1 0.00505284 0.7164179   NO   NO  NO 1
3 2 0.05276146 0.8533694   NO   NO  NO 1
4 3 0.14663061 0.9472385   NO   NO  NO 1
5 4 0.28358215 0.9949472   NO   NO  NO 1
6 5 0.47817625 1.0000000   NO   NO  NO 1
   x         LEX       UEX LABB UABB ZWI    e
1  0 0.000000000 0.2421417   NO   NO  NO 0.10
2  1 0.033389933 0.5677472   NO   NO  NO 0.10
3  2 0.121847735 0.7481841   NO   NO  NO 0.10
4  3 0.251815869 0.8781523   NO   NO  NO 0.10
5  4 0.432252823 0.9666101   NO   NO  NO 0.10
6  5 0.757858283 1.0000000   NO   NO  NO 0.10
7  0 0.000000000 0.4507197   NO   NO  NO 0.50
8  1 0.010012205 0.6655550   NO   NO  NO 0.50
9  2 0.073477832 0.8176210   NO   NO  NO 0.50
10 3 0.182378987 0.9265222   NO   NO  NO 0.50
11 4 0.334445049 0.9899878   NO   NO  NO 0.50
12 5 0.549280272 1.0000000   NO   NO  NO 0.50
13 0 0.000000000 0.5168931   NO   NO  NO 0.95
14 1 0.005318479 0.7127676   NO   NO  NO 0.95
15 2 0.054128982 0.8508479   NO   NO  NO 0.95
16 3 0.149152092 0.9458710   NO   NO  NO 0.95
17 4 0.287232382 0.9946815   NO   NO  NO 0.95
18 5 0.483106945 1.0000000   NO   NO  NO 0.95
19 0 0.000000000 0.5218238   NO   NO  NO 1.00
20 1 0.005052840 0.7164179   NO   NO  NO 1.00
21 2 0.052761458 0.8533694   NO   NO  NO 1.00
22 3 0.146630615 0.9472385   NO   NO  NO 1.00
23 4 0.283582147 0.9949472   NO   NO  NO 1.00
24 5 0.478176250 1.0000000   NO   NO  NO 1.00