Second order regular variation is a reenement of the concept of regular variation which is useful for studying rates of convergence in extreme value theory and asymptotic normality of tail estimators. For a distribution tail 1 ? F which possesses second order regular variation, we discuss how this property is inherited by 1 ? F 2 and 1 ? F 2. We also discuss the relationship of central limit be...

Background: Erythrocytes require an ability to deform and to withstand shear stress while negotiating the microcirculation. These properties are largely due to their excess surface area per volume and the characteristics of the membrane’s protein. Deficiencies of these proteins are associated with chronic haemolysis. Methods: This was a cross sectional  study aimed at determining the prevalenc...

We study a linear recursion with random Markov-dependent coefficients. In a “regular variation in, regular variation out” setup we show that its stationary solution has a multivariate regularly varying distribution. This extends results previously established for i.i.d. coefficients.

BACKGROUND E(epithelial)-cadherin is a vital cell adhesion protein that plays a critical role in morphogenesis. Previous studies of E-cadherin distribution in human embryos have produced equivocal results. METHODS Immunocytochemistry in conjunction with laser scanning confocal microscopy was used to detect E-cadherin in 97 human cleavage stage embryos and 35 blastocysts from normal and abnorm...

In this paper we study the distribution of eigenvalues of regular graphs , regular hypergraphs , and biregular bipartite graphs of given girth by considering the polynomials orthogonal with respect to the measures attached to the spectra of such graphs and to the continuous spectra of their ‘universal covers’ . Our estimates are tight for Biggs graphs and generalized polygons . We also give an ...

We give some characterizations of the exponential distribution based on the distributional properties and the expected values of record values; the index of record values has the geometric distribution.