ciBAx: Bayesian method of CI estimation with Beta prior distribution

In RajeswaranV/proportion: Inference on Single Binomial Proportion and Bayesian Computations

Bayesian method of CI estimation with Beta prior distribution

Description

Bayesian method of CI estimation with Beta prior distribution

Usage

ciBAx(x, n, alp, a, b)

Arguments

x	- Number of sucess
n	- Number of trials
alp	- Alpha value (significance level required)
a	- Shape parameter 1 for prior Beta distribution in Bayesian model. Can also be a vector of length n+1 priors.
b	- Shape parameter 2 for prior Beta distribution in Bayesian model. Can also be a vector of length n+1 priors.

Details

Highest Probability Density (HPD) and two tailed intervals are provided for the given x and n. based on the conjugate prior β(a, b) for the probability of success p of the binomial distribution so that the posterior is β(x + a, n - x + b).

Value

A dataframe with

x	- Number of successes (positive samples)
LBAQx	- Lower limits of Quantile based intervals
UBAQx	- Upper limits of Quantile based intervals
LBAHx	- Lower limits of HPD intervals
UBAHx	- Upper limits of HPD intervals

References

[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

See Also

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 Base methods of CI estimation given x & n: PlotciAllxg(), PlotciAllx(), PlotciEXx(), ciASx(), ciAllx(), ciEXx(), ciLRx(), ciLTx(), ciSCx(), ciTWx(), ciWDx()

Examples

x=5; n=5; alp=0.05; a=0.5;b=0.5;
ciBAx(x,n,alp,a,b)
x= 5; n=5; alp=0.05; a=c(0.5,2,1,1,2,0.5);b=c(0.5,2,1,1,2,0.5)
ciBAx(x,n,alp,a,b)

RajeswaranV/proportion documentation built on June 17, 2022, 9:11 a.m.