School Seminars and Colloquia

Characterization of Probability Distributions and Process Modeling

BELZ Lecture Series

by Prof Boyan Dimitrov, Kettering University (MI, USA)


Institution: The University of Melbourne
Date: Mon 15th March 2010
Time: 2:15 PM
Location: Room 712, Doug McDonell Bldg

Abstract: In this course, we will meet a new class of probability distributions and related random processes that arise in some real-life situations. Analysis of the properties of these distributions helps to understand the area of their applications and modeling power. We see how these properties are used to model various processes in economics, industry, demography, environmental studies, and how their use reflects on insurance, risk and cost analysis.

The course is mostly built on resent results obtained by the lecturer and is designed to give incentives and inspiration to students. Some open problems and further research directions will be presented, as well as various possible areas of applications.


A tentative list of topics to be covered:

1. The class of new probability distributions for modeling
environmental evolution with periodic behavior. A constructive approach.
2. Renewal and non-homogeneous Poisson processes generated by
distributions with periodic failure rate
3. Probability distributions in periodic random environment and their
applications
4. Periodic random environment generates compound counting processes
with amazing properties
5. Probability distributions with accumulating failure rates in
periodic random environment. Overall Population Growth in Periodic Environment
6. Ruin Modeling for Compound Non-Stationary Process with Periodic
Claim Intensity Rate
7. Uncertainty in periodic random environment. Modeling Uncertainty
in Periodic Random Environment: Applications to Environmental Studies
8. Bivariate probability distributions similar to exponential. The
Bivariate Probability Distributions with Periodic Failure Rate Via a Hyperbolic Differential Equation
9. Multiplicative Lack of Memory. Contorted uniform and Pareto
distributions
10. The ALM copula and its properties. Modeling dependence

For More Information: For more information contact Prof Kostya Borovkov email: borovkov@unimelb.edu.au