The construction of simple classification rules is a frequent problem in medical research. For example a difference in overall survival time may suggest distinct types, i.e. subgroups of patients, of diffuse large B-cell lymphoma identified by gene expression profiling. Maximally selected rank...

The partial attributable risk has been introduced as a tool for partitioning the responsibility for causing an adverse event between various risk factors. It has arisen from epidemiology but is also a valid general risk allocation concept which can for example be applied to data from customer...

Let ∈ ℂ be a nontrivial involution; i.e., = ≠ ±. We say that ∈ ℂ is -symmetric (-skew symmetric) if = ( = − ). Let be one of the following subsets of ℂ: (i) -symmetric matrices; (ii) Hermitian -symmetric matrices; (iii) -skew symmetric matrices; (iv) Hermitian -skew symmetric...

The class of multivariate elliptical distributions is generalized to allow for asymmetry preserving all the ordinary components, i.e. the generating variate, the location vector, and the dispersion matrix. A positive definite ML-estimator for the dispersion matrix which does not require any...

We strengthen a theorem of Kuijlaars and Serra Capizzano on the distribution of zeros of a sequence of orthogonal polynomials for which the coefficients in the three term recurrence relation are clustered at finite points. The proof uses a matrix argument motivated by a theorem of Tyrtyshnikov

The main result is lower estimation of remain term in the central limit theorem for a sum of the functions of disjoint uniform k-spacings. From this theorem the Lindeberg type condition of asymptotically normality and Berry-Esseen type result are obtained. The asymptotic properties of goodness...

In this paper we consider the problem —Δ = () + () in Ω, = 0 on , where λ ∈ (0, ∞), Ω is a strictly convex bounded and domain in R with ≥ 2, 1 < < 2, — 1 < < : (0, ∞) → (0, ∞) is a nonincreasing, and locally Lipchitz continuous function (that may be singular at 0) and : [0, ∞) → (0, ∞) is a contnuous and nondecreasing function satisfying inf<0 () > 0, 0 < lim∞ () < ∞. We prove that there exists λ* > 0 such that for 0 λ λ* the above problem has at least two positive solutions in Π (Ω) and that λ = 0 is a bifurcation point...</lim∞></<>

In this article, we address the problem of computing the distribution functions that can be expressed as discrete mixtures of continuous distributions. Examples include noncentral chisquare, noncentral beta, noncentral , noncentral and the distribution of squared sample multiple correlation. We...

The inversion formula for evaluation of the distribution of a linear combination of independent and random variables, respectively, is suggested. The method is applied to computing the exact confidence intervals for the common mean of several normal populations. This method is compared with the...