We propose a new procedure to perform Reduced Rank Regression (RRR) in nonGaussian contexts, based on Multivariate Dispersion Models. Reduced-Rank Multivariate Dispersion Models (RR-MDM) generalise RRR to a very large class of distributions, which include continuous distributions like the normal, Gamma, Inverse Gaussian, and discrete distributions like the Poisson and the binomial. A multivaria...

algorithm A recipe or set of instructions which, when followed precisely, will produce a desired result. binomial coefficient The binomial coefficient ( n k ) is the coefficient of x in the expansion of (1+x). It counts the number of ways of choosing k objects from a set of n objects. computer algebra system A computer package that enables the computer to do symbolic computations such as algebr...

Some stochastic theory is developed for monoecious populations of size N in which there are probabilities beta and 1 - beta of reproduction by selfing and by random mating. It is assumed that beta much greater than N-1. Expressions are derived for the inbreeding coefficient of one random individual and the coefficient of kinship of two random separate individuals at time t. The mean and between...

In this paper we establish lower bounds on information divergence from a distribution to certain important classes of distributions as Gaussian, exponential, Gamma, Poisson, geometric, and binomial. These lower bounds are tight and for several convergence theorems where a rate of convergence can be computed, this rate is determined by the lower bounds proved in this paper. General techniques fo...

We show that there can be no finite list of conditional independence relations which can be used to deduce all conditional independence implications among Gaussian random variables. To do this, we construct, for each n > 3 a family of n conditional independence statements on n random variables which together imply that X1⊥X2, and such that no subset have this same implication. The proof relies ...

Abstract. Empirical Bayes methods for Gaussian and binomial compound decision problems involving longitudinal data are considered. A new convex optimization formulation of the nonparametric (Kiefer-Wolfowitz) maximum likelihood estimator for mixture models is used to construct nonparametric Bayes rules for compound decisions. The methods are illustrated with some simulation examples as well as ...

1. P. Flajolet and A. Odlyzko, Singularity analysis of generating functions, SIAM J. Discrete Math. 3 (1990) 216–240. 2. R. E. Greenwood, The number of cycles associated with the elements of a permutation group, this MONTHLY 60 (1953) 407–409. 3. J. Konvalina, A unified interpretation of the binomial coefficients, the Stirling numbers, and the Gaussian coefficients, this MONTHLY 107 (2000) 901–...

We determine the liquid-state thermodynamics for a model energy landscape corresponding to soft spheres with a mean-field attraction. We consider two approximations, in which the distribution of potential energy minima is either Gaussian or binomial, and for each we calculate the liquid spinodal, binodal, and "effective" glass transition locus. The resulting models provide a unified description...

The summation formula within Pascal triangle resulting in the Fi-bonacci sequence is extended to the q-binomial coefficients q-Gaussian triangles [1, 2]. 1 Pisa historical remark The Fibonacci sequence origin is attributed and referred to the first edition (lost) of " Fiber abaci " (1202) by Leonardo Fibonacci [Pisano] (see second edition from 1228 reproduced as Il Liber Abaci di Leonardo Pisan...

For a delta operator aD − bD we find the corresponding polynomial sequence of binomial type and relations with Fuss numbers. In the case of D − 1 2D 2 we show that the corresponding Bessel–Carlitz polynomials are moments of the convolution semigroup of inverse Gaussian distributions. We also find probability distributions νt, t > 0, for which {yn(t)}, the Bessel polynomials at t, is the moment ...