cUmbrPK: Computes a critical value for the Mack-Wolfe Peak Known A_p...

In NSM3: Functions and Datasets to Accompany Hollander, Wolfe, and Chicken - Nonparametric Statistical Methods, Third Edition

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)

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.

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")

Author(s)

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.

Examples

##Hollander-Wolfe-Chicken Example 6.3 Fasting Metabolic Rate of White-Tailed Deer
cUmbrPK(.0101, c(7, 3, 5, 4, 4,3), peak=4)

NSM3 documentation built on Sept. 8, 2023, 5:52 p.m.