Binary segmentation and Bonferroni-type bounds
We introduce the function , where and are the pdf and cdf of , 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...
Bivariate Bonferroni inequalities.
Bivariate copulas, norms and non-exchangeability
The present paper is related to the study of asymmetry for copulas by introducing functionals based on different norms for continuous variables. In particular, we discuss some facts concerning asymmetry and we point out some flaws occurring in the recent literature dealing with this matter.
Bivariate copulas: Transformations, asymmetry and measures of concordance
The present paper introduces a group of transformations on the collection of all bivariate copulas. This group contains an involution which is particularly useful since it provides (1) a criterion under which a given symmetric copula can be transformed into an asymmetric one and (2) a condition under which for a given copula the value of every measure of concordance is equal to zero. The group also contains a subgroup which is of particular interest since its four elements preserve symmetry, the...
Bivariate negative binomial distribution of the Marshall-Olkin type
The bivariate negative binomial distribution is introduced using the Marshall-Olkin type bivariate geometrical distribution. It is used to the estimation of the distribution of the number of accidents in standard data.
Bochner property in Banach spaces
Bochner's theorem for finite-dimensional conelike semigroups.
Bonferroni-Galambos inequalities for partition lattices.
Bounded double square functions
We extend some recent work of S. Y. Chang, J. M. Wilson and T. Wolff to the bidisc. For , we determine the sharp order of local integrability obtained when the square function of is in . The Calderón-Torchinsky decomposition reduces the problem to the case of double dyadic martingales. Here we prove a vector-valued form of an inequality for dyadic martingales that yields the sharp dependence on p of in .
Bounded Laws of the Iterated Logarithm for Quadratic Forms in Gaussian Random Variables.
Boundedly Complete Families Which are Not Complete.
Bounds and asymptotic expansions for the distribution of the Maximum of a smooth stationary Gaussian process
This paper uses the Rice method [18] to give bounds to the distribution of the maximum of a smooth stationary Gaussian process. We give simpler expressions of the first two terms of the Rice series [3,13] for the distribution of the maximum. Our main contribution is a simpler form of the second factorial moment of the number of upcrossings which is in some sense a generalization of Steinberg et al.'s formula ([7] p. 212). Then, we present a numerical application and asymptotic expansions...
Bounds for distribution functions of sums of squares and radial errors.
Bounds for Median and 50 Percentage Point of Binomial and Negative Binomial Distribution.
Bounds for tail probabilities of the sample variance.
Bounds for the characteristic functions of the system of monomials in random variables and of its trigonometric analogue.
Bounds for the Difference Between Median and Mean of Beta and Negative Binomial Distributions.
Bounds of general Fréchet classes
This paper deals with conditions of compatibility of a system of copulas and with bounds of general Fréchet classes. Algebraic search for the bounds is interpreted as a solution to a linear system of Diophantine equations. Classical analytical specification of the bounds is described.
Bounds on expectations of record range and record increment from distributions with bounded support.