Check this site:
http://www.firstpr.com.au/dsp/pink-noise/.
Although the answer to your question isn't explicitly stated, the
paper states that pink noise can be made from adding multiple white
noise sources that have been low pass filtered, (Voss-McCartney
algorithm of adding multiple white noise sources at lower and lower
octaves). Filtering should not affect the amplitude distribution.
You'd expect the summations would also not affect the probability
distributions. All this assumes that your white noise sources have
gaussian (normal) amplitude distribution.
Other articles
http://stason.org/TULARC/entertainment/audio/general/13-4-What-is-whi...
suggest pink noise is coloured by frequency distribution, and
amplitude distribution is determined by the noise mechanism - it may
or may not be gaussian. See also:
http://en.wikipedia.org/wiki/White_noise
Similarily, white noise doesn't need to be gaussian!
This referencehttp://books.google.ca/books?id=PImqHW34Bt0C&pg=PA163&lpg=PA163&ots=b...
says that pink or bandwidth limited white noise is "pseudo gaussian",
in that the integral of the noise doesn't work out to be exactly zero
as true gaussian noise should (but its close).
There is a mention in the rec.audio.faq: "Another term you'll hear
about is Gaussian noise - this is noise with a Gaussian amplitude
probability density. Gaussian noise has the amazing property that
linearly filtering it preserves its Gaussian amplitude density and
that sums of Gaussian random variables are again Gaussian. The two
terms shouldn't be confused. It is possible to have Gaussian white or
pink noise."
Several hours of searching through papers really didn't provide
much enlightenment, especially with the useful looking ones needing a
payment before you could get at them! My best search results were
using "pink noise gaussian" as a criteria. Some of the hits don't seem
to be very authoritative!
Why the need for probability distribution? Was it to determine
probabilities of the multiples of rms levels (ie., prob that gausssian
signal exceeds 3*rms is 0.37%
http://en.wikipedia.org/wiki/Normal_distribution)?
Paul G.