Automated Derivation of Exact Formulas for the Average, Variance, and Higher Moments
Of Combinatorial Statistics given by Bivariate Rational Functions
By Manuel Kauers, Gleb Pogudin and Doron Zeilberger
.pdf
.ps
.tex
Written: Dec. 15, 2016
Maple package
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BiVariateMoms.txt,
a Maple package to automatically derive explicit expressions for the expectation, variance, and higher moments
of combinatorial random variables whose generating functions are given by bivariate generating functions.
Sample Input and Output Files for the Maple package BiVariateMoms.txt
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If you want to see a computer-generated article about the average, variance, and the moments up to the 6th, of the
random variable "number of 2's" defined on the set of compositions of n, only using 1's and 2's
the
input file generates
output file.
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If you want to see a computer-generated article about the average, variance, and the moments up to the 6th, of the
random variable "number of Heads" defined on the set outcomes of n coin-tosses of a fair coin
the
input file generates
output file.
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If you want to see a computer-generated article about the average, variance, and the moments up to the 4th, of the
random variable "number of monomers" defined on the set of monomer-dimer tilings of a 2 by n rectangle , 4 by n rectangle , and 6 by n
rectangle,
the
input file generates
output file.
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If you want to see graphs of the function x vs. limit of log(a(n,n*x))/n as n goes to infinity,
where a(n,m) is the coefficient of tnwm in the Maclaurin expansion of the
rational function f(t,w), for various rational functions,
the
input file generates
output file.
Personal Journal of Shalosh B. Ekhad and Doron Zeilberger
Doron Zeilberger's Home Page