# 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

## 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

 `1` ```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")

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

 ```1 2``` ```##Hollander-Wolfe-Chicken Example 6.3 Fasting Metabolic Rate of White-Tailed Deer cUmbrPK(.0101, c(7, 3, 5, 4, 4,3), peak=4) ```

### Example output

```Loading required package: combinat

Attaching package: ‘combinat’

The following object is masked from ‘package:utils’:

combn