empirical_cdfi

Empirical inverse cumulative distribution function

Syntax

   x = empirical_cdfi(P,X,ptails,ksmooth)

Arguments

See also Common variable names and data structures.

input

   P          vector of cumulative distribution probabilities
   X          vector of sample statistics
   ptails     Pareto tails lower and upper probabilities (default: no Pareto tails)
   ksmooth    use kernel smoothing to estimate cdf (default: no smoothing)

output

   x          vector of statistic values

Description

Returns the empirical inverse cumulative distribution function estimated from sample statistics in vector X, evaluated at probabilities in the vector P. To calculate the critical value for a significance level alpha, X should be drawn from the appropriate null distribution and P set to 1-alpha (see empirical_cval). For confidence intervals at level alpha, X should be drawn from the appropriate sample distribution and P set to alpha for the lower bound and 1-alpha for the upper bound (see empirical_confint).

Uses the Matlab Statistics Toolbox paretotails class to estimate the inverse cdf. Pareto tails for the corresponding cumulative distribution may be specified by the 2-vector ptails, with lower and upper cumulative probabilities in ptails(1) and ptails(2) respectively [where |0 ptails(1) < ptails(2) <= 1|]. If the ksmooth flag is set, then kernel smoothing is used to estimate the cdf, otherwise simple midpoint interpolation; see <matlab:doc('paretotails') paretotails for details.

See also

empirical_cdf | empirical_pval | empirical_confint | empirical_cval | paretotails