Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899272 | Journal of Mathematical Analysis and Applications | 2018 | 9 Pages |
Abstract
Let dâN and let γiâ[0,â), xiâ(0,1) be such that âi=1d+1γi=Mâ(0,â) and âi=1d+1xi=1. We prove thataâ¦Î(aM+1)âi=1d+1Î(aγi+1)âi=1d+1xiaγi is completely monotonic on (0,â). 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
Authors
Frédéric Ouimet,