We introduce a one-parameter deformation of the Wishart-Laguerre or chiral ensembles of positive definite random matrices with Dyson index β = 1, 2 and 4. Our generalised model has a fat-tailed distribution while preserving the invariance under orthogonal, unitary or symplectic transformations. The spectral properties are derived analytically for finite matrix size N ×M for all three β, in term...

This paper develops and compares specification tests for parametric duration models estimated with censored data. The tests are based on generalized residuals (the integrated hazard), which is exponentially distributed if the model is correctly specified. I present several conditional moment tests based on the generalized residuals: a raw moments test, a test based on Laguerre polynomials, and ...

We consider several generalizations of rook polynomials. In particular we develop analogs of the theory of rook polynomials that are related to general Laguerre and Charlier polynomials in the same way that ordinary rook polynomials are related to simple Laguerre polynomials.

This paper presents a method for approximating spherical tessellations, the edges of which are geodesic arcs, using spherical Laguerre Voronoi diagrams. The approximation method involves fitting the polyhedron corresponding to the spherical Laguerre Voronoi diagram to the observed tessellation using optimization techniques.

We describe the first non-classical 4-dimensional Minkowski planes and show that they have 6-dimensional automorphism groups. These planes are obtained by a construction of Schroth [18] from generalized quadrangles associated with the semiclassical 4-dimensional Laguerre planes. All 4-dimensional Minkowski planes that can be obtained in this way from the semiclassical 4-dimensional Laguerre pla...

Fractional differentiation systems are characterized by the presence of non-exponential aperiodic multimodes. Although rational orthogonal bases can be used to model any L2[0,∞[ system, they fail to quickly capture the aperiodic multimode behavior with a limited number of terms. Hence, fractional orthogonal bases are expected to better approximate fractional models with fewer parameters. Intuit...

Analysis of function spaces and special functions are closely related to the representation theory of Lie groups. We explain here the connection between the Laguerre functions, the Laguerre polynomials, and the Meixner-Pollacyck polynomials on the one side, and highest weight representations of Hermitian Lie groups on the other side. The representation theory is used to derive differential equa...

where α + β + 1 > β > 1 −m, σ + 1 > α + β > 0, m is a positive integer, and 0 < h < ∞, 0 ≤ b <∞, and h and b are finite constants. L n [(x + b)h] is a Laguerre polynomial, An are unknown coefficients, and f (x) and g(x) are prescribed functions. Srivastava [5, 6] has solved the following dual series equations: ∞ ∑ n=0 AnL (α) n (x) Γ(α+n+ 1) = f (x), 0 < x < a, (1.3) ∞ ∑ n=0 AnL (σ) n (x) Γ(α+n...

The explicit double sum for the associated Laguerre polynomials is derived combinatorially. The moments are described using certain statistics on permutations and permutation tableaux. Another derivation of the double sum is provided using only the moment generating function.

The support of the orthogonality measure of so-called little q-Laguerre polynomials {ln(.; a|q)}n=0, 0 < q < 1, 0 < a < q−1, is given by Sq = {1, q, q, . . .} ∪ {0}. Based on a method of MÃlotkowski and Szwarc we deduce a parameter set which admits nonnegative linearization. We additionally use this result to prove that little q-Laguerre polynomials constitute a so-called Faber basis in C(Sq).