R: Weighted Empirical Cumulative Distribution Function

ewcdf {spatstat} | R Documentation

## 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"` (if `normalise=TRUE`) and `"stepfun"`. The class `ewcdf` has methods for `print` and `quantile`. 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)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

### See Also

`ecdf`.

`quantile.ewcdf`

### Examples

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

[Package spatstat version 1.63-3 Index]