From dmurdoch at pair.com  Tue Feb  3 14:49:30 2004
From: dmurdoch at pair.com (Duncan Murdoch)
Date: Tue Feb  3 14:49:45 2004
Subject: [Rd] request for comments --- package "distr" --- S4 Classes for
	Distributions
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	<Pine.WNT.4.58.0402031228430.164@auk>
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On Tue, 3 Feb 2004 12:31:10 +0000 (GMT Standard Time), Prof Brian D
Ripley <ripley@stats.ox.ac.uk> wrote :

>On Tue, 3 Feb 2004, Duncan Murdoch wrote:
>
>> On Tue, 03 Feb 2004 09:45:52 +0000, Matthias Kohl
>> <Matthias.Kohl@uni-bayreuth.de> wrote:
>>
>> >I think the most common example is the Cantor distribution.
>>
>> That's the most common 1-dimensional singular distribution, but higher
>> dimensional distributions are much more commonly singular.  For
>> example, mixed continuous-discrete distributions, and other
>> distributions whose support is of lower dimension than the sample
>> space, e.g. X ~ N(0,1), Y=X.
>
>The most common 1d singular distribution is probably a lifetime with an
>atom at zero.

We differ in notation.  I wouldn't call that one singular; I'd call it
mixed continuous and discrete, because the distribution function is a
sum of an absolutely continuous function and a step function.  But in
the measure theory sense, it's singular w.r.t. Lebesgue measure.

Duncan


[Rd] request for comments --- package "distr" --- S4 Classes for Distributions
Duncan Murdoch