On a Conjecture of Feige for Discrete Log-Concave Distributions
| Autor: | Alqasem, Abdulmajeed, Aravinda, Heshan, Marsiglietti, Arnaud, Melbourne, James |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A remarkable conjecture of Feige (2006) asserts that for any collection of $n$ independent non-negative random variables $X_1, X_2, \dots, X_n$, each with expectation at most $1$, $$ \mathbb{P}(X < \mathbb{E}[X] + 1) \geq \frac{1}{e}, $$ where $X = \sum_{i=1}^n X_i$. In this paper, we investigate this conjecture for the class of discrete log-concave probability distributions and we prove a strengthened version. More specifically, we show that the conjectured bound $1/e$ holds when $X_i$'s are independent discrete log-concave with arbitrary expectation. Comment: 11 pages |
| Databáze: | arXiv |
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