Colloquia — Summer 2001
Monday, July 2, 2001
| Title |
Some New Distributions in Statistics |
| Speaker |
Dr. Saralees Nadarajah
University of California, Santa Barbara |
| Time |
3:00-4:00 |
| Place |
PHY 130 |
| Sponsor |
Professor A.N.V. Rao |
| Note |
Speaker is a candidate for Asst. Prof. in Statistics. |
Abstract
I shall talk about two of my most recent research products:
- the Planck distribution (joint work with Professor Leipnik, Department of
Mathematics, University of California, Santa Barbara);
- some new elliptical distributions (joint work with Professor Kotz, Department
of Engineering Management and Systems Engineering, George Washington University,
Washington, D.C.).
Planck is a well-known physicist. He discovered a distribution that generalizes
the well-known Gamma distribution. This distribution, which we refer to as the
Planck distribution, has been around in the physics literature for many years.
However, to the best of our knowledge, it does not appear to have been noted
in the statistics literature. In the first part of my talk, I shall introduce
the Planck distribution and derive its basic properties such as the characteristic
function, moments, likelihood, maximum likelihood equations and the Fisher information
matrix. Calculations involve the "Lerch" function.
The last twenty years have seen a vigorous development of multivariate elliptical
distributions as direct generalizations of the multivariate normal distribution,
which has dominated statistical theory and applications for almost a century.
One of the most attractive elliptical distributions known in the statistics
literature is the so-called Kotz type distribution (named after my co-author).
It provides a most natural generalization of the multivariate normal distribution.
In the second part of my talk, I shall note that the Kotz type distribution
can be interpreted as being generated by the Type III extreme value distribution.
Based on this observation, I shall develop two new elliptical distributions
based on the Type I and Type II extreme value distributions and show results
on their structural properties.