empericalBA: The empirical Bayesian approach for Beta-Binomial model
In proportion: Inference on Single Binomial Proportion and Bayesian Computations

Description Usage Arguments Details Value References See Also Examples

The empirical Bayesian approach for Beta-Binomial model

1	empericalBA(n, alp, sL, sU)

`n`	- Number of trials
`alp`	- Alpha value (significance level required)
`sL`	- Lower support for MLE optimization
`sU`	- Upper support for MLE optimization

Highest Probability Density (HPD) and two tailed intervals are provided for all x = 0, 1, 2 ..n based on empirical Bayesian approach for Beta-Binomial model. Lower and Upper support values are needed to obtain the MLE of marginal likelihood for prior parameters.

A dataframe with

`x`	- Number of successes (positive samples)
`pomean`	- Posterior mean
`LBAQ`	- Lower limits of Quantile based intervals
`UBAQ`	- Upper limits of Quantile based intervals
`LBAH`	- Lower limits of HPD intervals
`UBAH`	- Upper limits of HPD intervals

[1] 1998 Lehmann EL and Casella G Theory of Point Estimation, 2nd ed Springer, New York

Other Miscellaneous functions for Bayesian method: empericalBAx, probPOSx, probPOS, probPREx, probPRE

sL=runif(1,0,2)				#Lower and upper of Support for MLE optimization
sU=runif(1,sL,10)
n= 5; alp=0.05
empericalBA(n,alp,sL,sU)

  x pomean  LEBAQ  UEBAQ  LEBAH  UEBAH
1 0 0.1383 0.0050 0.4350 0.0000 0.3726
2 1 0.2669 0.0419 0.6029 0.0176 0.5534
3 2 0.4315 0.1384 0.7558 0.1276 0.7432
4 3 0.5685 0.2442 0.8616 0.2568 0.8724
5 4 0.7331 0.3971 0.9581 0.4466 0.9824
6 5 0.8617 0.5650 0.9950 0.6274 1.0000