Related papers: Euler-Frobenius numbers and rounding
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
We propose a new approach to quantize the marginals of the discrete Euler diffusion process. The method is built recursively and involves the conditional distribution of the marginals of the discrete Euler process. Analytically, the method…
From a suitable integral representation of the Laplace transform of a positive semi-definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for…
Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation.…
This paper generalises the exponential family GLM to allow arbitrary distributions for the response variable. This is achieved by combining the model-assisted regression approach from survey sampling with the GLM scoring algorithm, weighted…
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous…
Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation.…
This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the $n$ partitions of the interval $[0,W_n]$ are independent and identically distributed…
Eulerian polynomials record the distribution of descents over permutations. Caylerian polynomials likewise record the distribution of descents over Cayley permutations, where a Cayley permutation is a word of positive integers such that if…
This paper surveys recent developments in the sampling discretization of integral and uniform norms for functions in general finite-dimensional spaces. These results generalize the classical Marcinkiewicz-Zygmund inequalities for…
We introduce and study deferred N\"{o}rlund statistical convergence in probability, mean of order $r,$ distribution, and study the interrelation among them. Based upon the proposed method to illustrate the findings, we present new Korovkin…
We present a computational framework for efficient learning, sampling, and distribution of general Bayesian posterior distributions. The framework leverages a machine learning approach for the construction of normalizing flows for the…
This paper examines the statistical properties of a distributional form that arises from pooled testing for the prevalence of a binary outcome. Our base distribution is a two-parameter distribution using a prevalence and excess intensity…
The main object of this paper is to investigate a new class of the generalized Hurwitz type poly-Bernoulli numbers and polynomials from which we derive some algorithms for evaluating the Hurwitz type poly-Bernoulli numbers and polynomials.…
The projected normal distribution, also known as the angular Gaussian distribution, is obtained by dividing a multivariate normal random variable $\mathbf{x}$ by its norm $\sqrt{\mathbf{x}^T \mathbf{x}}$. The resulting random variable…
Goulden and Jackson introduced a very powerful method to study the distributions of certain consecutive patterns in permutations, words, and other combinatorial objects which is now called the cluster method. There are a number of natural…
In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…
We study linear recurrences of Eulerian type of the form \[ P_n(v) = (\alpha(v)n+\gamma(v))P_{n-1}(v) +\beta(v)(1-v)P_{n-1}'(v)\qquad(n\ge1), \] with $P_0(v)$ given, where $\alpha(v), \beta(v)$ and $\gamma(v)$ are in most cases polynomials…
The Poisson-binomial distribution is useful in many applied problems in engineering, actuarial science, and data mining. The Poisson-binomial distribution models the distribution of the sum of independent but not identically distributed…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…