[Gnuplot-info] Proper gaussian weight for smooth kdensity with logscale x?

[Rhys U. <rhy...@gm...>]

When plotting with 'smooth kdensity' I must provide 1/number-of-points
as the second plotting column to get a normalized histogram.  Does
that scaling factor need to change to get a properly normalized
histogram when using a logarithmic x axis?  I should be able to sort
through this myself, but my head's not working today.

More concretely, should the (1.0/nsamp) factor be modified in some
fashion to obtain a normalized kernel density estimate for the second
plot below?

set print "random.tmp"
mean  = 5
nsamp = 10000
do for [i=1:nsamp] {
    print sprintf("%8.5g", invnorm(rand(0)) + mean)
}
unset print

set term postscript

# Normalized per 'help smooth kdensity'
set output "regular.ps"
plot "random.tmp" using 1:(1.0/nsamp) smooth kdensity

# How should this be normalized?
set logscale x
set output "logscale.ps"
plot "random.tmp" using 1:(1.0/nsamp) title 'Logscale x' smooth kdensity

Thank you,
Rhys