pmsd: Median scaled difference probabilities and quantiles

Description

Cumulative lower tail probability and quantile for median of scaled differences.

Usage

pmsd(q, n, sd=1, scale=TRUE)
	qmsd(p, n, sd=1, scale=TRUE)

Arguments

Vector of quantiles.

Vector of probabilities.

Scalar: number of observations from which msd was calculated.

Standard deviation, used to scale q.

scale

If scale is TRUE, sd is divided by sqrt(2) prior to calculating p or q.

Value

A vector of length length(p) or length(q) of quantiles or probabilities respectively.

Details

pmsd and qmsd implement exact (for even n) or approximate (odd n) probabilities and quantiles for the median scaled difference applied to a single observation in a normal distribution. n is the number of observations in the data set of interest and not the degrees of freedom or number of differences (msd for a value x[i] in a set of n observations involves n-1 scaled differences). The probabilities are calculated using quadrature integration over a distribution of an order statistic, and may be quite slow (seconds for a vector of several hundred 100 values of q on an Intel x86 machine running at 1GHz). qmsd is obtained even more slowly by root-finding from pmsd using uniroot. Note that both functions are appropriate for the distribution of single values. If seeking an outlier test, adjust p for n comparisons before applying qmsd.

Examples

Run this code

data(Pb)
  msd(Pb$value)          # Uses mad(Pb$value) as scale estimate
  msd(Pb$value, Pb$u)    # Scales differences using standard uncertainties