[S] Density function of sine function?

David F. Parkhurst (parkhurs@indiana.edu)
Wed, 17 Jun 1998 10:33:19 -0500


Consider something (e.g., daylength) that varies more or less
sinusoidally. If you think about a density curve for daylengths,
you find that there are lots of long days (centered around
midsummer) and lots of short days in the winter, but relatively few
medium-length days (because daylength changes rapidly from day to
day around the equinoxes). One way to illustrate this is with:

x <- (0:1000)*pi/500
y <- 12*sin(x)+6

plot(density(y))

I'd like, analytically, to find the density function for values that
vary sinusoidally. Can anyone think of a way to do that?

Thanks.

Dave Parkhurst
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