# PofCSt: Probability of Correct Selection (PCS) for Selecting t out of... In PCS: Calculate the Probability of Correct Selection (PCS)

 PofCSt R Documentation

## 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

` 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. https://docs.google.com/a/biola.edu/viewer?a=v&pid=sites&srcid=YmlvbGEuZWR1fGphc29ud2lsc29ufGd4OjJmYTY2YTJjY2EwYjg2ZmY
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`

PCS documentation built on June 21, 2022, 1:05 a.m.