Mathematics Colloquium

Department of Mathematics
University of Nebraska at Omaha

WHEN:
Wednesday September 7, 2005 at 2:30 PM

WHERE:
Durham Science Center, Room 255

WHAT:

Steve From

UNO - Mathematics

will give a talk on

SOME NEW BOUNDS ON THE DEVIATION PROBABILITY FOR SUMS OF NON-NEGATIVE RANDOM VARIABLES USING UPPER POLYNOMIALS AND PROBABILITY GENERATING FUNCTIONS

ABSTRACT:
Probabilities involving the sum of independent but not identically distributed random variables are not easy to compute in general. A number of inequalities exist which provide bounds on these probabilities. I will discuss some old inequalities and some new inequalities I have found during my research this past year. The new inequalities use methods for constructing upper bound polynomials and upper probability generating functions for various functions. The coefficients of the upper bound polynomials satisfy certain conic section relationships. I will present numerical examples comparing these bounds, since analytic comparisons are not always possible

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