Glossary Dilation matrix A 2× 2 matrix M is called a dilation matrix if all the entries of M are integers and all the eigenvalues of M are greater than one in modulus. Isotropic dilation matrix A dilation matrix M is said to be isotropic if M is similar to a diagonal matrix and all its eigenvalues have the same modulus. Wavelet system A wavelet system is a collection of square integrable functi...

We define generalized bivariate polynomials, from which specifying initial conditions the bivariate Fibonacci and Lucas polynomials are obtained. Using essentially a matrix approach we derive identities and inequalities that in most cases generalize known results. 1 Antefacts The generalized bivariate Fibonacci polynomial may be defined as Hn(x, y) = xHn−1(x, y) + yHn−2(x, y), H0(x, y) = a0, H1...

Let U and V be two independent normal random variables, and consider two new random variables X and Y of the form X = aU + bV, Y = cU + dV, where a, b, c, d, are some scalars. Each one of the random variables X and Y is normal, since it is a linear function of independent normal random variables.† Furthermore, because X and Y are linear functions of the same two independent normal random variab...

• We review the current state of statistical modeling of asymptotically independent data. Our discussion includes necessary and sufficient conditions for asymptotic independence, results on the asymptotic independence of statistics of interest, estimation and inference issues, joint tail modeling, and conditional approaches. For each of these topics we give an account of existing approaches and...

This paper is concerned with the nonnegativity preserving interpolation of data on rectangular grids. The function is a kind of bivariate rational interpolation spline with parameters, which is C1 in the whole interpolation region. Sufficient conditions are derived on coefficients in the rational spline to ensure that the surfaces are always nonnegative if the original data are nonnegative. The...

In this paper we build on previous work for estimation of the bivariate distribution of the time variables T1 and T2 when they are observable only on the condition that one of the time variables, say T1, is greater than (lefttruncation) or less than (right truncation) some observed time variable C1. In this paper, we introduce several results based on the In uence Curve (which we derive in this...

W automate the bivariate change-of-variables technique for bivariate continuous random variables with arbitrary distributions. This extends the algorithm for univariate change-of-variables devised by Glen et al. [Glen, A. G., L. M. Leemis, J. H. Drew. 1997. A generalized univariate change-of-variable transformation technique. INFORMS J. Comput. 9(3) 288–295]. Our transformation procedure handle...

In this paper we consider the general problem of estimating the tail of a bivariate distribution. An extension of the threshold method for extreme values is developed, using a two-dimensional version of the Pickands-Balkema-de Hann Theorem. We construct a two-dimensional tail estimator and we provide its asymptotic properties. The dependence structure between the marginals is described by a cop...

Inspired by the discussion in [5], we study the multiplicative complexity and the rank of the multiplication in the local algebras Rm;n = k[x; y]=(xm+1; yn+1) and Tn = k[x; y]=(xn+1; xny; : : : ; yn+1) of bivariate polynomials. We obtain the lower bounds (2 13 o(1)) dimRm;n and (2 12 o(1)) dim Tn for the multiplicative complexity of the multiplication in Rm;n and Tn, respectively. On the other ...