From p.dalgaard at biostat.ku.dk  Tue Feb  3 13:21:24 2004
From: p.dalgaard at biostat.ku.dk (Peter Dalgaard)
Date: Tue Feb  3 13:22:49 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: <x2ptcw2w1n.fsf@biostat.ku.dk>

Duncan Murdoch <dmurdoch@pair.com> writes:

> 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.

I don't think that qualifies as continuous, does it? Not in the sense
that the distribution function is continuous, surely. 

The Cantor distribution is the one that has the "devils staircase" as
distribution function, right? Continuous, differentiable almost
everywhere but the derivative is always 0. (Take an interval, divide
in three, let F(0) = 0, F(1) = 1, F(x)=.5 on the middle third, and
define the outer thirds recursively.)

-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard@biostat.ku.dk)             FAX: (+45) 35327907


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