ewcdf: Weighted Empirical Cumulative Distribution Function

In spatstat.geom: Geometrical Functionality of the 'spatstat' Family

Weighted Empirical Cumulative Distribution Function

Description

Compute a weighted version of the empirical cumulative distribution function.

Usage

ewcdf(x, weights = NULL, normalise=TRUE, adjust=1)

Arguments

x	Numeric vector of observations.
weights	Optional. Numeric vector of non-negative weights for x. Defaults to equal weight 1 for each entry of x.
normalise	Logical value indicating whether the weights should be rescaled so that they sum to 1.
adjust	Numeric value. Adjustment factor. The weights will be multiplied by adjust.

Details

This is a modification of the standard function ecdf allowing the observations x to have weights.

The weighted e.c.d.f. (empirical cumulative distribution function) Fn is defined so that, for any real number y, the value of Fn(y) is equal to the total weight of all entries of x that are less than or equal to y. That is Fn(y) = sum(weights[x <= y]).

Thus Fn is a step function which jumps at the values of x. The height of the jump at a point y is the total weight of all entries in x number of tied observations at that value. Missing values are ignored.

If weights is omitted, the default is equivalent to ecdf(x) except for the class membership.

The result of ewcdf is a function, of class "ewcdf", inheriting from the classes "ecdf" (only if normalise=TRUE) and "stepfun".

The class ewcdf has methods for print, quantile and mean.

The inherited classes ecdf and stepfun have methods for plot and summary.

Value

A function, of class "ewcdf", inheriting from "ecdf" (if normalise=TRUE) and "stepfun".

Author(s)

\spatstatAuthors

.

See Also

ecdf.

quantile.ewcdf, mean.ewcdf.

Integrals with respect to the weighted cumulative distribution function can be computed using stieltjes.

Examples

   x <- rnorm(100)
   w <- runif(100)
   plot(e <- ewcdf(x,w))
   e

spatstat.geom documentation built on Oct. 20, 2023, 9:06 a.m.