This paper continues a series of results begun by a l’Hospital type rule for monotonicity, which is used here to obtain refinements of the Eaton-Pinelis inequalities for sums of bounded independent… (More)

Let (S0, S1, . . . ) be a supermartingale relative to a nondecreasing sequence of σ-algebras (H60,H61, . . . ), with S0 6 0 almost surely (a.s.) and differences Xi := Si − Si−1. Suppose that for… (More)

Elsewhere we developed rules for the monotonicity pattern of the ratio r := f/g of two differentiable functions on an interval (a, b) based on the monotonicity pattern of the ratio ρ := f ′/g′ of the… (More)

Let f andg be differentiable functions on an interval (a, b), and let the derivative g′ be positive on(a, b). The main result of the paper implies that, if f(a+) = g(a+) = 0 and f ′ g′ is increasing… (More)

Abstract: Let (S0, S1, . . . ) be a supermartingale relative to a nondecreasing sequence of σ-algebras H60, H61, . . . , with S0 6 0 almost surely (a.s.) and differences Xi := Si − Si−1. Suppose that… (More)

An O(n) test for polygon convexity is stated and proved. It is also proved that the test is minimal in a certain exact sense. Everyone knows a convex polygon when one sees it. Yet, to deal with the… (More)

Abstract: Pearson’s R is the most common correlation statistic, used mainly in parametric settings. Most common among nonparametric correlation statistics are Spearman’s S and Kendall’s T . We show… (More)

An explicit representation of an arbitrary zero-mean distribution as the mixture of (at-most-)two-point zero-mean distributions is given. Based in this representation, tests for (i) asymmetry… (More)

The most widely used evolutionary model for phylogenetic trees is the equal-rates Markov (ERM) model. A problem is that the ERM model predicts less imbalance than observed for trees inferred from… (More)