Brad C. Johnson

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In this short note, we establish the uniform integrability and pointwise convergence of an (unbounded) family of polynomials on the unit interval that arises in work on statistical density estimation using Bernstein polynomials. These results are proved by first establish-ing/generalizing some combinatorial and probability inequalities that rely on a new(More)
In this short note, we establish the uniform integrability and pointwise convergence of an (unbounded) family of polynomials on the unit interval that arises in work on statistical density estimation using Bernstein polynomials. These results are proved by first establishing/generalizing some combinatorial and probability inequalities that rely on a new(More)
Empirical testing of computer generated pseudo-random sequences is widely practiced. Extensions to the <italic>coupon collector's</italic> and <italic>gap</italic> tests are presented that examine the distribution and independence of radix-<italic>b</italic> digit patterns in sequences with modulo of the form <italic>b<supscrpt>w</supscrpt></italic>. An(More)
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