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