# covpBA: Coverage Probability of Bayesian method In proportion: Inference on Single Binomial Proportion and Bayesian Computations

## Description

Coverage Probability of Bayesian method

## Usage

 `1` ```covpBA(n, alp, a, b, t1, t2, a1, a2) ```

## Arguments

 `n` - Number of trials `alp` - Alpha value (significance level required) `a` - Beta parameters for hypo "p" `b` - Beta parameters for hypo "p" `t1` - Lower tolerance limit to check the spread of coverage Probability `t2` - Upper tolerance limit to check the spread of coverage Probability `a1` - Beta Prior Parameters for Bayesian estimation `a2` - Beta Prior Parameters for Bayesian estimation

## Details

Evaluation of Bayesian Highest Probability Density (HPD) and two tailed intervals using coverage probability, root mean square statistic, and the proportion of proportion lies within the desired level of coverage for the Beta - Binomial conjugate prior model for the probability of success `p`.

## Value

A dataframe with

 `method` Both Quantile and HPD method results are returned `MeanCP` Coverage Probability `MinCP ` Minimum coverage probability `RMSE_N ` Root Mean Square Error from nominal size `RMSE_M ` Root Mean Square Error for Coverage Probability `RMSE_MI ` Root Mean Square Error for minimum coverage probability `tol ` Required tolerance for coverage probability

## 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

Other Basic coverage probability methods: `PlotcovpAS`, `PlotcovpAll`, `PlotcovpBA`, `PlotcovpEX`, `PlotcovpLR`, `PlotcovpLT`, `PlotcovpSC`, `PlotcovpTW`, `PlotcovpWD`, `covpAS`, `covpAll`, `covpEX`, `covpLR`, `covpLT`, `covpSC`, `covpTW`, `covpWD`
 ```1 2 3 4 5``` ```## Not run: n= 10; alp=0.05; a=1;b=1; t1=0.93;t2=0.97;a1=1;a2=1 covpBA(n,alp,a,b,t1,t2,a1,a2) ## End(Not run) ```