# stieltjes: Compute Integral of Function Against Cumulative Distribution In spatstat: Spatial Point Pattern Analysis, Model-Fitting, Simulation, Tests

## Description

Computes the Stieltjes integral of a function f with respect to a function M.

## Usage

 `1` ```stieltjes(f, M, ...) ```

## Arguments

 `f` The integrand. A function in the R language. `M` The cumulative function against which `f` will be integrated. An object of class `"fv"` or `"stepfun"`. `...` Additional arguments passed to `f`.

## Details

This command computes the Stieltjes integral

I = integral f(x) dM(x)

of a real-valued function f(x) with respect to a nondecreasing function M(x).

One common use of the Stieltjes integral is to find the mean value of a random variable from its cumulative distribution function F(x). The mean value is the Stieltjes integral of f(x)=x with respect to F(x).

The argument `f` should be a `function` in the R language. It should accept a numeric vector argument `x` and should return a numeric vector of the same length.

The argument `M` should be either a step function (object of class `"stepfun"`) or a function value table (object of class `"fv"`, see `fv.object`). Objects of class `"stepfun"` are returned by `ecdf`, `ewcdf`, `spatialcdf` and other utilities. Objects of class `"fv"` are returned by the commands `Kest`, `Gest`, etc.

## Value

A list containing the value of the Stieltjes integral computed using each of the versions of the function `M`.

## Author(s)

\spatstatAuthors

.

`fv.object`, `Gest`
 ``` 1 2 3 4 5 6 7 8 9 10``` ``` # estimate cdf of nearest neighbour distance in redwood data G <- Gest(redwood) # compute estimate of mean nearest neighbour distance stieltjes(function(x){x}, G) # estimated probability of a distance in the interval [0.1,0.2] stieltjes(function(x,a,b){ (x >= a) & (x <= b)}, G, a=0.1, b=0.2) # stepfun example H <- spatialcdf(bei.extra\$elev, normalise=TRUE) stieltjes(function(x){x}, H) ```