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)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.
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")
Harding, E. F. "An efficient, minimal-storage procedure for calculating the Mann-Whitney U, generalized U and similar distributions." Applied statistics (1984): 1-6.
# NOT RUN {
##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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