# PdofCSt.T1or2: Exact PCS, when selecting t=1 or t=2 or more populations In PCS: Calculate the probability of correct selection (PCS)

## Description

PdofCSt.T1or2 calls PofCSt to implement the d-best PCS formula for the case of t=1 or t=2 populations. It is called by PdofCSt.cyc2, which implements the d-best PCS formula for general t populations. PofCSGt calls PofCSt to implement the G-best formula for general t. These functions are modular and implement the time reduction techniques of Cui and Wilson (2007).

## Usage

 ```1 2 3``` ```PdofCSt.T1or2(theta, T, d, m = 20, tol = 1e-08) PdofCSt.cyc2(theta, T, d, m = 20, tol = 1e-08) PofCSGt(theta, T, Gd, m = 20, tol = 1e-08) ```

## 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 `d` The d-best selection parameter (scalar) `Gd` The G-best selection parameter (scalar) `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

## 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

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