(July 4th) Characterization of Probability Distributions in Terms of Their Moments

  • Subject
    Characterization of Probability Distributions in Terms of Their Moments
  • Date
    2019.07.04 (Thu) 14:00
  • Speaker
    Jordan Stoyanov (Bulgarian Academy of Sciences)
  • Place
    Wooribyul Seminar Room(E3-2, #2201)
Overview: 

Our discussion will be on distributions, continuous or discrete, with finite all moments of positive integer order. Any such a distribution is either uniquely determined by its moments (M-determinate), or it is non-unique (M-indeterminate). We are going to explain why some distributions are M-determinate, and others are M-indeterminate. The uniqueness, or M-determinacy, is an important property from both theoretical and applied point of view. In particular, the M-determinacy is an essential requirement for the validity of a fundamental limit theorem. We will describe the current state of arts and concentrate on a variety of checkable conditions which are either sufficient or necessary for uniqueness or for non-uniqueness (Cramer, Carleman, Hardy, Krein, Lin, rate of growth of moments, etc.)

Besides the moments, we will exploit the cumulants/semi-invariants to establish a non-conventional limit theorem. We illustrate ideas and results by examples based on distributions such that Normal, Poisson, Exponential, Lognormal. It time permits, some challenging open questions will be outlined.  

Profile: 
Honorary Professor, Bulgarian Academy of Sciences, Sofia, Bulgaria
Visiting Professor, Shandong University, Jinan, China
Formerly with Newcastle University, UK (1998-2015)
Author of 80 papers and 5 books including Counterexamples in Probability (Third ed.) Dover Publications, New York, December 2013
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