10 citations · 34 across the 19 of their papers we have counts for
9 papers · 1 filter
Some inequalities on Binomial and Poisson probabilities
Robbert Fokkink, Symeon Papavassiliou, Christos Pelekis
Let and be independent random variables, assuming values in the set of non-negative integers, and suppose further that both and are integers…
Optimizing stakes in simultaneous bets
Robbert Fokkink, Ludolf Meester, Christos Pelekis
We want to find the convex combination of iid Bernoulli random variables that maximizes for a given threshold~. Csóka conjectured that such an is a…
On the Shannon entropy of the number of vertices with zero in-degree in randomly oriented hypergraphs
Christos Pelekis
Suppose that you have colours and mutually independent dice, each of which has sides. Each dice lands on any of its sides with equal probability. You may colour the sid…
Lower bounds on binomial and Poisson tails: an approach via tail conditional expectations
Christos Pelekis
We derive upper bounds on the tail conditional expectation of binomial and Poisson random variables. Those upper bounds are subsequently employed to the problem of obtaining non-as…
A lower bound on the probability that a binomial random variable is exceeding its mean
Christos Pelekis, Jan Ramon
We provide a lower bound on the probability that a binomial random variable is exceeding its mean. Our proof employs estimates on the mean absolute deviation and the tail condition…
Hölder-type inequalities and their applications to concentration and correlation bounds
Christos Pelekis, Jan Ramon, Yuyi Wang
Let be -valued random variables having a dependency graph . We show that \[ \mathbb{E}\left[\prod_{v\in V} Y_{v} \right] \leq \prod_{v\in V} \left\{…
Hoeffding's inequality for sums of weakly dependent random variables
Christos Pelekis, Jan Ramon
We provide a systematic approach to deal with the following problem. Let be, possibly dependent, -valued random variables. What is a sharp upper bound on th…
On the Bernstein-Hoeffding method
Christos Pelekis, Jan Ramon, Yuyi Wang
We show that the Bernstein-Hoeffding method can be employed to a larger class of generalized moments. This class includes the exponential moments whose properties play a key role i…
Bernoulli trials of fixed parity, random and randomly oriented graphs
Christos Pelekis
Suppose you can color \emph{biased} coins with colors, all coins having the same bias. It is forbidden to color both sides of a coin with the same color, but all other colo…