CL_quantile

Description

• Evaluates quantiles of a data set.

  Let F be the empirical cumulative distribution function associated with the data set X. The quantity (x) that is computed is such that:

  F(x) = p (p: probability in [0,1]).

  The method used to calculate sample quantiles is the same as in R-project (method number 5):

  For a data set containing N elements, quantiles are computed as follows:

  1) The sorted values in X are considered as the (0.5/N), (1.5/N), ..., ((N-0.5)/N) quantiles.

  2) Linear interpolation is used to compute quantiles for probabilities between (0.5/N) and ((N-0.5)/N)

  3) The minimum or maximum values in X are assigned to quantiles for probabilities outside that range.

  Note: This method is used in Matlab's quantile function as well.

Parameters

X:

Data set (1xN)

p:

Probabilities (1xP)

x:

Quantiles (1xP)

Authors

• CNES - DCT/SB

Bibliography

• 1) R: A Language and Environment for Statistical Computing; http://cran.r-project.org/doc/manuals/fullrefman.pdf.

Examples

// Random gaussian sample N = 10000; m = 0; // mean sd = 1; // standard deviation X = grand(1,N,"nor",m,sd); // Probability values p = [0.6827, 0.9545, 0.9973]; x = CL_quantile(abs(X),p); // close to [1,2,3]*sd