cUmbrPK: Computes a critical value for the Mack-Wolfe Peak Known A_p distribution.
Description
This function computes the critical value for the Mack-Wolfe Peak Known A_p distribution at (or typically in the "Exact" case, close to) the given alpha level. The function generalizes Harding's (1984) algorithm to quickly generate the distribution.
Usage
cUmbrPK(alpha, n, peak=NA, method=NA, n.mc=10000)
Value
Returns a list with "NSM3Ch6c" class containing the following components:
n
number of observations in the k data groups
cutoff.U
upper tail cutoff at or below user-specified alpha
true.alpha.U
true alpha level corresponding to cutoff.U (if method="Exact")
Arguments
alpha
A numeric value between 0 and 1.
n
A vector of numeric values indicating the size of each of the k data groups.
peak
An integer representing the known peak among the data groups.
method
Either "Exact" or "Asymptotic", indicating the desired distribution. When method=NA, if sum(n)<=200, the "Exact" method will be used to compute the A_p distribution. Otherwise, the "Asymptotic" method will be used.
n.mc
Not used. Only included for standardization with other critical value procedures in the NSM3 package.
Author
Grant Schneider
References
Harding, E. F. "An efficient, minimal-storage procedure for calculating the Mann-Whitney U, generalized U and similar distributions." Applied statistics (1984): 1-6.