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August, 1995 Precision Calculation of Distributions for Trimmed Sums
Sandor Csorgo, Gordon Simons
Ann. Appl. Probab. 5(3): 854-873 (August, 1995). DOI: 10.1214/aoap/1177004708


Recursive methods are described for computing the frequency and distribution functions of trimmed sums of independent and identically distributed nonnegative integer-valued random variables. Surprisingly, for fixed arguments, these can be evaluated with just a finite number of arithmetic operations (and whatever else it takes to evaluate the common frequency function of the original summands). These methods give rise to very accurate computational algorithms that permit a delicate numerical investigation, herein described, of Feller's weak law of large numbers and its trimmed version for repeated St. Petersburg games. The performance of Stigler's theorem for the asymptotic distribution of trimmed sums is also investigated on the same example.


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Sandor Csorgo. Gordon Simons. "Precision Calculation of Distributions for Trimmed Sums." Ann. Appl. Probab. 5 (3) 854 - 873, August, 1995.


Published: August, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0846.60018
MathSciNet: MR1359832
Digital Object Identifier: 10.1214/aoap/1177004708

Primary: 60E99

Keywords: 60-04 , recursive algorithms for distributions , St. Petersburg game , Trimmed sums on nonnegative integers

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.5 • No. 3 • August, 1995
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