# Probability of correct selection (PCS) for selecting t out of k populations

### 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.

### See Also

`PdofCSt.T1or2`

, `PdofCSt.cyc2`

, `PofCSGt`