# stieltjes

0th

Percentile

##### Compute Integral of Function Against Cumulative Distribution

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

Keywords
spatial, math
##### Usage
stieltjes(f, M, ...)
##### Arguments
f
The integrand. A function in the Rlanguage.
M
The cumulative function against which f will be integrated. An object of class "fv".
...
Additional arguments passed to f.
##### Details

This command computes the Stieltjes integral $$I = \int f(x) dM(x)$$ 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 Rlanguage. It should accept a numeric vector argument x and should return a numeric vector of the same length.

The argument M should be a function value table (object of class "fv", see fv.object). Such objects are returned by the commands link{Kest}, Gest, etc.

##### Value

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

fv.object, Gest

• stieltjes
##### Examples
data(redwood)
# estimate cdf of nearest neighbour distance
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)
Documentation reproduced from package spatstat, version 1.17-0, License: GPL (>= 2)

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