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We introduce the function $Z (x; ξ, ν) : = \int_{- \infty}^{x} ϕ (t - ξ) \cdot Φ (ν t) d t$ , where $ϕ$ and $Φ$ are the pdf and cdf of $N (0, 1)$ , respectively. We derive two recurrence formulas for the effective computation of its values. We show that with an algorithm for this function, we can efficiently compute the second-order terms of Bonferroni-type inequalities yielding the upper and lower bounds for the distribution of a max-type binary segmentation statistic in the case of small samples (where asymptotic results do not work), and in general for max-type random variables...

Composition sum identities related to the distribution of coordinate values in a discrete simplex.

Milson, R. (2000)

The Electronic Journal of Combinatorics [electronic only]

Densité et dimension

Patrick Assouad (1983)

Annales de l'institut Fourier

Une partie $𝒮$ de $2^{X}$ est appelée une classe de Vapnik-Cervonenkis si la croissance de la fonction $Δ^{𝒮} : r \to Sup {| A \cap | | A \subset X, | A | = r}$ est polynomiale; ces classes se trouvent être utiles en Statistique et en Calcul des Probabilités (voir par exemple Vapnik, Cervonenkis [V.N. Vapnik, A.YA. Cervonenkis, Theor. Prob. Appl., 16 (1971), 264-280], Dudley [R.M. Dudley, Ann. of Prob., 6 (1978), 899-929]).Le présent travail est un essai de synthèse sur les classes de Vapnik-Cervonenkis. Mais il contient aussi beaucoup de résultats nouveaux,...

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A characterization of the simplex.

A combinatorial inequality. (Eine kombinatorische Ungleichung.)

A discontinuity in the distribution of fixed point sums.

A generalized formula of Hardy.

A multinomial extension of an inequality of Haber.

An extension of a criterion for unimodality.

An inequality related to two integer sequences satisfying an order condition.

Aperiodic words on three symbols. II.

Asymptotic expansions for the coefficients of analytic generating functions.

Bender's generalized q-binominal Vandermonde convolution.

Binary segmentation and Bonferroni-type bounds

Composition sum identities related to the distribution of coordinate values in a discrete simplex.

Densité et dimension

Durfee polynomials.

Enumerating permutations that avoid three term arithmetic progressions.

Errata: Oprava k môjmu článku 'O niektorých kombinatorických nerovnostiach'

From recursions to asymptotics: On Szekeres' formula for the number of partitions.

Generalized Newton-like inequalities.

Generalized $λ$ -Newton inequalities revisited.

Good lower and upper bounds on binomial coefficients.

Currently displaying 1 – 20 of 56