# pmsd.xnorm: Internal functions for package RKC. In metRology: Support for Metrological Applications

## Description

The following functions are used internally by pmsd and qmsd.

## Usage

 `1` ```.pmsd.xnorm(q, x, n, sd = 1, scale = FALSE) ```

## Arguments

 `q` vector of quantiles `x` scalar value `n` number of observations in data set to which msd is applied `sd` a standard deviation `sd` Standard deviation, used to scale q. `scale` If scale is `TRUE`, `sd` is divided by `sqrt(2)`.

## Details

Provides the distribution function for msd given a value x, using the cumulative probability for an order statistics givn in Mood, Graybill and Boes (1974) pp252ff. `pmsd` integrates (using `integrate`) over x to obtain the distribution function for msd for random x.

## Value

A vector of probabilities

## Author(s)

S Ellison [email protected]

## References

Mood, Graybill and Boes (1974) pp252ff

## See Also

`pmsd`, `msd`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```## The function is currently defined as function(q, x, n, sd=1, scale=FALSE) { if(scale) sd <- sd/sqrt(2) pxnorm<-function(q,x,sd=1) ifelse(q>0, pnorm(x+q, 0, sd)-pnorm(x-q, 0, sd), 0) Fy<-rep(0, length(q)) n.med<-floor(n/2) #exact for odd samples, low for even #Note that for n values there are n-1 differences, #so an even-n case is an odd-median case ph<-pxnorm(q,x,sd) for(j in n.med:(n-1)) Fy <- Fy + choose(n-1,j) * (ph^j) * (1-ph)^(n-j-1) return(Fy) } ```

metRology documentation built on Sept. 9, 2017, 3:02 a.m.