Article ID Journal Published Year Pages File Type
8899272 Journal of Mathematical Analysis and Applications 2018 9 Pages PDF
Abstract
Let d∈N and let γi∈[0,∞), xi∈(0,1) be such that ∑i=1d+1γi=M∈(0,∞) and ∑i=1d+1xi=1. We prove thata↦Γ(aM+1)∏i=1d+1Γ(aγi+1)∏i=1d+1xiaγi is completely monotonic on (0,∞). This result generalizes the one found by Alzer [2] for binomial probabilities (d=1). As a consequence of the log-convexity, we obtain some combinatorial inequalities for multinomial coefficients. We also show how the main result can be used to derive asymptotic formulas for quantities of interest in the context of statistical density estimation based on Bernstein polynomials on the d-dimensional simplex.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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