I. Pinelis

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20242026

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math.PR2026

Equi-dependence implying independence

Iosif Pinelis

It is shown that, if an event $A$ has the same conditional probability in each trial in an infinite sequence of Bernoulli trials, then $A$ is independent of each trial. More genera…

math.PR2026

One-sided concentration near the mean of log-concave distributions

Iosif Pinelis

A lower bound on the probability $P (0 < X < I^´)$ for all real $I^´ > 0$ and all random variables $X$ with log-concave p.d.f.'s such that $E X = 0$ and $E X^{2} = 1$ is obtained.

math.PR2025

Does the Convex Order Between the Distributions of Linear Functionals Imply the Convex Order Between the Probability Distributions Over $R^{d}$ ?

Iosif Pinelis

It is shown that the convex order between the distributions of linear functionals does not imply the convex order between the probability distributions over $R^{d}$ if $d\ge2…

Equi-dependence implying independence

One-sided concentration near the mean of log-concave distributions

Does the Convex Order Between the Distributions of Linear Functionals Imply the Convex Order Between the Probability Distributions Over Rd?

Does the Convex Order Between the Distributions of Linear Functionals Imply the Convex Order Between the Probability Distributions Over $R^{d}$ ?