# spCdf: (Weighted empirical) cumulative distribution function In simPop: Simulation of Synthetic Populations for Survey Data Considering Auxiliary Information

## Description

Compute a (weighted empirical) cumulative distribution function for survey or population data. For survey data, sample weights are taken into account.

## Usage

 `1` ```spCdf(x, weights = NULL, approx = FALSE, n = 10000) ```

## Arguments

 `x` a numeric vector. `weights` an optional numeric vector containing sample weights. `approx` a logical indicating whether an approximation of the cumulative distribution function should be computed. `n` a single integer value; if `approx` is `TRUE`, this specifies the number of points at which the approximation takes place (see `approx`).

## Details

Sample weights are taken into account by adjusting the step height. To be precise, the weighted step height for an observation is defined as its weight divided by the sum of all weights.

If requested, the approximation is performed using the function `approx`.

## Value

A list of class `"spCdf"` with the following components:

 `x` a numeric vector containing the x-coordinates. `y` a numeric vector containing the y-coordinates. `approx` a logical indicating whether the coordinates represent an approximation.

## Author(s)

Andreas Alfons and Stefan Kraft

## References

A. Alfons, M. Templ (2011) Simulation of close-to-reality population data for household surveys with application to EU-SILC. Statistical Methods & Applications, 20 (3), 383–407. doi: 10.1007/s10260-011-0163-2

`spCdfplot`, `ecdf`, `approx`
 ```1 2 3``` ```data(eusilcS) cdfS <- spCdf(eusilcS\$netIncome, weights = eusilcS\$rb050) plot(cdfS, type="s") ```