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The p-variate gamma distribution in the sense of Krishnamoorthy and Parthasarathy exists for all positive integer degrees of freedom d and at least for all real values d > p-2, p > 1. For special structures of the "associated" covariance…
Differential invariants for the maximal Lie invariance group of the Korteweg-de Vries equation are computed using the moving frame method and compared with existing results. Closed forms of differential invariants of any order are presented…
In this paper, we study the number of real roots of random trigonometric polynomials with iid coefficients. When the coefficients have zero mean, unit variance and some finite high moments, we show that the variance of the number of real…
This paper proposes a generalisation of the Pearson type II distribution, which shall termed Pearson Type II-Riesz distribution, based in the Kotz-Riesz distribution. Specifically, the central nonsingular matricvariate generalised Pearson…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is discussed. A wide set of measurable quantities ("invariant moments") whose expectation value…
We consider finite point subsets (distributions) in compact metric spaces. In the case of general rectifiable metric spaces, non-trivial bounds for sums of distances between points of distributions and for discrepancies of distributions in…
A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…
We prove $q$-variation estimates, $q>2$, on $\ell^{p}$ spaces for averages along primes (with $1<p<\infty$) and polynomials (with $\big| \frac1p - \frac12 \big| < \frac{1}{2(d+1)}$, where $d$ is the degree of the polynomial). This improves…
Normal variance mixtures are a class of multivariate distributions that generalize the multivariate normal by randomizing (or mixing) the covariance matrix via multiplication by a non-negative random variable W. The multivariate t…
In this letter we derive the $(n-1)$-dimensional distribution corresponding to a $n$-dimensional i.i.d. Normal standard vector $Z=(Z_1,Z_2,\ldots,Z_n)$ subjected to the weighted sum constraint $\sum_{i=1}^n w_i Z_i=c$, $w_i\neq 0$. We first…
We prove that for a positive integer $k$ the primes in certain kinds of intervals can not distribute too 'uniformly' among the reduced residue classes modulo $k$. Hereby, we prove a generalization of a conjecture of Recaman and establish…
The theory of admissible distributions over a weight-space of one-variable was studied by Amice--V\'{e}lu and played important roles in the cyclotomic Iwasawa theory of non-ordinary p-adic Galois representations. In this article, we discuss…
We derive the Wick theorem for the q-Exponential distribution. We use the theorem to derive an algorithm for finding parameters of the correlation matrix of q-Exponentialy distributed random variables given empirical spectral moments of the…
We revisit multivariate extreme value theory modeling by emphasizing multivariate regular variations and the multivariate Breiman Lemma. This allows us to recover in a simple framework the most popular multivariate extreme value…
We investigate the regularising properties of singular kernels at the level of germs, i.e. families of distributions indexed by points in $\mathbb{R}^d$. First we construct a suitable integration map which acts on general coherent germs.…
The family of multivariate skew-normal distributions has many interesting properties. It is shown here that these hold for a general class of skew-elliptical distributions. For this class, several stochastic representations are established…
The parton distribution functions determined by CTEQ at low $Q^2$ are used as inputs to test the validity of the valon model. The valon distributions in a nucleon are first found to be nearly $Q$ independent. The parton distribution in a…
Considering discrete models, the univariate framework has been studied in depth compared to the multivariate one. This paper first proposes two criteria to define a sensu stricto multivariate discrete distribution. It then introduces the…
We construct the multivariate probability distributions (P\'olya, inverse P\'olya, hypergeometric and negative hypergeometric) from the generalized quantum algebra. Moreover, we derive the bivariate probability distributions and determine…
The assumption of normality in data has been considered in the field of statistical analysis for a long time. However, in many practical situations, this assumption is clearly unrealistic. It has recently been suggested that the use of…