Abstract
In this article, we show that a linear combination X ˜ of n independent, unbiased Bernoulli random variables { X k } can match the first 2 n moments of a random variable Y which is uniform on an interval. More generally, for each p ⩾ 2 , each X k can be uniform on an arithmetic progression of length p. All values of X ˜ lie in the range of Y, and their ordering as real numbers coincides with dictionary order on the vector ( X 1 , … , X n ) . The construction involves the roots of truncated q-exponential series. It applies to a construction in numerical cubature using error-correcting codes [G. Kuperberg, Numerical cubature using error-correcting codes, arXiv: math.NA/0402047]. For example, when n = 2 and p = 2 , the values of X ˜ are the 4-point Chebyshev quadrature formula.
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