Michael Grabchak, UNC Charlotte

*Title: *Three Upsilon Transforms Related to Tempered Stable Distributions

Assistant Professor, Department of Mathematics and Statistics

AUTHOR

October 11, 2017 by Michael Grabchak

Categories: Probability Seminar

Michael Grabchak, UNC Charlotte

*Title: *Three Upsilon Transforms Related to Tempered Stable Distributions

September 25, 2017 by Michael Grabchak

Categories: Probability Seminar

Michael Grabchak, UNC Charlotte

*Title: *On the consistency of the MLE for selfdecomposable distributions and processes

September 11, 2017 by Michael Grabchak

Categories: Probability Seminar

Kevin McGoff, UNC Charlotte

*Title: *Dynamical systems and stochastic processes Part 2

September 04, 2017 by Michael Grabchak

Categories: Probability Seminar

Kevin McGoff, UNC Charlotte

*Title: *Dynamical systems and stochastic processes

April 25, 2017 by Michael Grabchak

Categories: Probability Seminar

Stanislav Molchanov, UNC Charlotte

*Title: *A Review of the Anderson Parabolic Model: Known Results and Open Problems

April 11, 2017 by Michael Grabchak

Categories: Probability Seminar

Stanislav Molchanov, UNC Charlotte

*Title: *Turing Formula

April 04, 2017 by Michael Grabchak

Categories: Probability Seminar

Michael Grabchak, UNC Charlotte

*Title:* Limit Theorems for Mobility Models

March 15, 2017 by Michael Grabchak

Categories: Probability Seminar

Zhiyi Zhang UNC Charlotte

*Title: *Statistical Implications of Turing’s Formula

Abstract: This talk is organized into three parts.

1. Turing’s formula is introduced. Given an iid sample from an countable alphabet under a probability distribution, Turing’s formula (introduced by Good (1953), hence also known as the Good-Turing formula) is a mind-bending non-parametric estimator of total probability associated with letters of the alphabet that are NOT represented in the sample. Many of its statistical properties were not clearly known for a stretch of nearly sixty years until recently. Some of the newly established results, including various asymptotic normal laws, are described.

2. Turing’s perspective is described. Turing’s formula brought about a new perspective (or

a new characterization) of probability distributions on general countable alphabets. The

new perspective in turn provides a new way to do statistics on alphabets, where the usual statistical concepts associated with random variables (on the real line) no longer exist, for example, moments, tails, coefficients of correlation, characteristic functions don’t exist on alphabets (a major challenge of modern data sciences). The new perspective, in the form of entropic basis, is introduced.

3. Several applications are presented, including estimation of information entropy and diversity indices.

March 14, 2017 by Michael Grabchak

Categories: Probability Seminar

Stanislav Molchanov, UNC Charlotte

*Title: *A Central Limit Theorem for the Missing Mass

March 01, 2017 by Michael Grabchak

Categories: Probability Seminar

Stanislav Molchanov, UNC Charlotte

*Title: *On the Missing Mass Problem in the Continuous Case Part 3