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

Description Usage Arguments Details Value Author(s) References See Also Examples

The following functions are used internally by pmsd and qmsd.

1	.pmsd.xnorm(q, x, n, sd = 1, scale = FALSE, method="exact")

`q`	vector of quantiles
`x`	scalar value
`n`	number of observations in data set to which msd is applied
`sd`	Standard deviation, used to scale q.
`scale`	If scale is `TRUE`, `sd` is divided by `sqrt(2)`.
`method`	Controls method of calculation; see `pmsd` for 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.

A vector of probabilities

S Ellison s.ellison@lgc.co.uk

Mood, Graybill and Boes (1974) pp252ff

pmsd, msd

## 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)

  }