Re: [Gnuplot-info] Integration of kdensity plots

[Ethan M. <eam...@gm...>]

On Fri, Jan 30, 2015 at 8:10 AM,  <lyn...@fr...> wrote:
>
> It   seems  approximate  integration  is  possible  with  gnuplot,  as  in  eg
> bivariat.dem. I'd like to use tha to get integrations of a kdensity plot  that
> is based on measurements.
> Fort  that,  is it possible to get the function that is behind a kdensity plot
> or would I have to construct it by hand for the given data? Or is it  possible
> to directly get the integral value of a specified interval?

The kdensity plot produced by gnuplot is a sum of Gaussians.
I.e. it is a plot of the first equation given on the Wikipedia page
for "kernel density estimation" where K(x) = φ(x) = normal density
function.

It sounds like the quantity you want is a trivial variant of that
which substitutes the cumulative normal distribution function norm(x)
for φ(x).  It is probably easier to calculate the sum directly from
the data than it is to program an approximate integration based on an
intermediate plot.

    Ethan