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.
cUmbrPK(alpha, n, peak=NA, method=NA, n.mc=10000)Returns a list with "NSM3Ch6c" class containing the following components:
number of observations in the k data groups
upper tail cutoff at or below user-specified alpha
true alpha level corresponding to cutoff.U (if method="Exact")
A numeric value between 0 and 1.
A vector of numeric values indicating the size of each of the k data groups.
An integer representing the known peak among the data groups.
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.
Not used. Only included for standardization with other critical value procedures in the NSM3 package.
Grant Schneider
Harding, E. F. "An efficient, minimal-storage procedure for calculating the Mann-Whitney U, generalized U and similar distributions." Applied statistics (1984): 1-6.
##Hollander-Wolfe-Chicken Example 6.3 Fasting Metabolic Rate of White-Tailed Deer
cUmbrPK(.0101, c(7, 3, 5, 4, 4,3), peak=4)
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