Precision calculation of distributions for trimmed sums
Effective recursive methods for computing the frequency and distribution functions for trimmed sums of i.i.d. nonnegative integer-valued random variables are obtained which require just a finite number of arithmetic operations and also avoid mixed signs. Consequently, these recursions give rise to very accurate computational algorithms. They are used to carry out a detailed numerical investigation of Feller's weak law of large numbers and its trimmed version for the accumulated payoffs in independent repetitions of the famous St. Petersburg game. The accuracy of approximations for the distributions of trimmed sums obtained via Stigler's limit theorem for these sums is also studied on the same example.
nonnegative integer-valued random variables
scientific article; zbMATH DE number 854868