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

[Duncan Murdoch]

On Tue, 3 Feb 2004 12:31:10 +0000 (GMT Standard Time), Prof Brian D
Ripley <ripley at 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 at 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