Probability of correct selection (PCS) for selecting t out of k populations
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.
PofCSt(theta, T, m, tol = 1e-07)
Vector of statistics (or parameters) from which it is desired to select the top t of them
The number of statistics (or parameters) desired to be selected
Number of nodes employed in the Gauss-Hermite quadrature
Tolerance parameter to set the cut-off level for the inclusion of additional probability components in PCS
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).
The probability of correct selection.
Jason Wilson, <email@example.com>
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.
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.
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