The University of Liverpool
Department of Mathematical Sciences
Division of Statistics and Probability
SEMINAR
Moment Analysis of Distributions
Jordan Stoyanov
University of Newcastle
Wednesday, 8th February 2006, 2pm
The Whittaker Room (211)
Abstract:
The main discussion will be on distributions and their characterisation
properties in terms of the moments: the classical problem of moments. We
analyse both cases when the solution is M-unique or M-nonunique
(M-determinate or M-indeterminate). Several recent results will be
reported.
We concentrate on transformations of random data (Box-Cox transformations).
The data may come from random variables or from stochastic processes.
Surprisingly (or not) in many cases we have to deal with distributions
which are M-nonunique. The analysis of such distributions is based on two
new notions, Stieltjes class and its Index of dissimilarity. We describe a
general method for constructing Stieltjes classes and give detailed
illustrations involving popular distributions. We also calculate the Index
of dissimilarity and give a statistical interpretation.
Then we turn to discuss why the uniqueness and non-uniqueness of
distributions are important for both practice and theory? We give some
illustrations. The first is about properties of distributions such as
symmetry, unimodality and infinite divisibility. The second is from
stochastic financial modelling (e.g Black-Scholes type models): option
pricing problem and a related stochastic optimization problem. The third
one deals with identifiability of mixtures of a class of distributions.
If time permits some open and challenging problems will be briefly
outlined.
The talk will be addressed to professionals and doctoral students in the
area of statistics, probability, mathematics (theory and/or applications).
Following the talk, tea and biscuits will be available in Room 304
ALL WELCOME
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Ingrid Harper
University of Liverpool
Department of Mathematical Sciences
Division of Statistics and Probability
Mathematical Sciences Building
Peach Street
Liverpool L69 7ZL
Tel: 0151 794 4751
Fax: 0151 794 4754
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