The Annals of Applied Probability

Precision Calculation of Distributions for Trimmed Sums

Sandor Csorgo and Gordon Simons

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Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 5, Number 3 (1995), 854-873.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177004708

Digital Object Identifier
doi:10.1214/aoap/1177004708

Mathematical Reviews number (MathSciNet)
MR1359832

Zentralblatt MATH identifier
0846.60018

JSTOR
links.jstor.org

Subjects
Primary: 60E99: None of the above, but in this section

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

Citation

Csorgo, Sandor; Simons, Gordon. Precision Calculation of Distributions for Trimmed Sums. Ann. Appl. Probab. 5 (1995), no. 3, 854--873. doi:10.1214/aoap/1177004708. https://projecteuclid.org/euclid.aoap/1177004708


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