Re: [boost] [math/staticstics/design] How best tonamestatisticalfunctions?

From: Topher Cooper (topher_at_[hidden])
Date: 2006-07-14 11:45:41

At 10:45 AM 7/14/2006, Paul Bristow wrote:
>So how to we find out what is considered "standard" - ask you? consult
>Mathemetica's documentation?textbooks..?  Is there agreement on standard?  I
>suspect so, but

You'll find a lot of variation in how the distribution parameters are 
expressed for some distributions but all single-dimensional 
distribution families are pretty unambiguous on this point.  There 
are some number of parameters that indexes a specific distribution 
from a family of distributions.  Random variables are associated with 
that distribution.  There is a quantity, "x" representing possible 
values for such a random variable.  The integral of the PDF of x (or 
sum for a discrete variate/distribution) from -infinity to t is the 
CDF for that distribution at t.  It is the probability that a random 
variabe will have a value less than or equal to t.  The inverse CDF 
sometimes called the "quantile" in statistical packages (a usage 
taken from statistics in the social sciences) is the functional 
inverse of the CDF function.  It's value for a particular "p" is the 
value for t with a probability p that a random variable will be less 
than it.  I don't think you'll find any real disagreement in any 
source about this.

I've finally figured out that you guys are not really talking about 
functional inverses at all.  You're saying "inverse" when you mean a 
parameter estimator.  As I posted a little while ago, that's a much 
more elaborate issue than you think it is.

Topher