# PofCSt: Probability of correct selection (PCS) for selecting t out of... In PCS: Calculate the probability of correct selection (PCS)

## Description

Implementation of the Gupta & Liang (1998) formula for computing the probability of correct selection (PCS) for selecting t out of k populations. The results are exact up to a user-settable tolerance parameter. This function is modular and is called by PdofCSt.T1or2, PdofCSt.cyc2, and PofCSGt.

## Usage

 `1` ``` PofCSt(theta, T, m, tol = 1e-07) ```

## Arguments

 `theta` Vector of statistics (or parameters) from which it is desired to select the top t of them `T` The number of statistics (or parameters) desired to be selected `m` Number of nodes employed in the Gauss-Hermite quadrature `tol` Tolerance parameter to set the cut-off level for the inclusion of additional probability components in PCS

## Details

The analytic formula for computing PCS for t of k populations is an integral whose integrad is the product of normal densities. This function obtains the appropriate values and computes the integral using a Gauss-Hermite quadrature. See equation 2.4 of Gupta (1998).

## Value

The probability of correct selection.

## Author(s)

Jason Wilson, <jason.wilson@biola.edu>

## References

Cui, X. and Wilson, J. 2007. On How to Calculate the Probability of Correct Selection for Large k Populations. University of California, Riverside Statistics Department Technical Report 297. http://www.bubbs.biola.edu/~jason.wilson/Article2_tech_techreport.pdf
Gupta, S.S. and Liang, T.C. 1998. Simultaneous lower confidence bounds for probabilities of correct selections. Journal of Statistical Planning and Inference. 72(1-2), 279-290.

`PdofCSt.T1or2`, `PdofCSt.cyc2`, `PofCSGt`