From ripley at stats.ox.ac.uk  Tue Feb  3 13:31:10 2004
From: ripley at stats.ox.ac.uk (Prof Brian D Ripley)
Date: Tue Feb  3 13:31:47 2004
Subject: [Rd] request for comments --- package "distr" --- S4 Classes
	for Distributions
In-Reply-To: <7b2v1018thc0oecs1sdq1rm447cvlmag5f@4ax.com>
References: <D7A3CFD7825BD6119B880002A58F06C20680ADF6@groexmb02.pfizer.com>
	<x2ad413yue.fsf@biostat.ku.dk> <401F6DD0.2080602@uni-bayreuth.de>
	<7b2v1018thc0oecs1sdq1rm447cvlmag5f@4ax.com>
Message-ID: <Pine.WNT.4.58.0402031228430.164@auk>

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.

I think the question was about a continuous but not absolutely continuous
distribution, and indeed the Cantor distribution is the standard example
in theory courses.

-- 
Brian D. Ripley,                  ripley@stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595


[Rd] request for comments --- package "distr" --- S4 Classes for Distributions
Prof Brian D Ripley