| stieltjes {spatstat.univar} | R Documentation |
Compute Integral of Function Against Cumulative Distribution
Description
Computes the Stieltjes integral
of a function f with respect to a function M.
Usage
stieltjes(f, M, ...)
Arguments
f |
The integrand. A function in the R language. |
M |
The cumulative function against which |
... |
Additional arguments passed to |
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 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"
).
Objects of class "stepfun" are returned by
ecdf, ewcdf,
and other utilities.
Value
A list containing the value of the Stieltjes integral
computed using each of the versions of the function M.
Author(s)
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner rolfturner@posteo.net and Ege Rubak rubak@math.aau.dk.
Examples
x <- runif(100)
w <- runif(100)
H <- ewcdf(x, w)
stieltjes(function(x) { x^2 }, H)