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In this article, a discrete analogue of continuous Teissier distribution is presented. Its several important distributional characteristics have been derived. The estimation of the unknown parameter has been done using the method of maximum…
In this work, we consider an extension of graphical models to random graphs, trees, and other objects. To do this, many fundamental concepts for multivariate random variables (e.g., marginal variables, Gibbs distribution, Markov properties)…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
We outline some of Chris Wallace's contributions to pseudo-random number generation. In particular, we consider his idea for generating normally distributed variates without relying on a source of uniform random numbers, and compare it with…
We establish a general inequality on the Poisson space, yielding an upper bound for the distance in total variation between the law of a regular random variable with values in the integers and a Poisson distribution. Several applications…
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…
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in…
Random graphs with a given degree sequence are often constructed using the configuration model, which yields a random multigraph. We may adjust this multigraph by a sequence of switchings, eventually yielding a simple graph. We show that,…
In this paper, we propose a new and unified approach for nonparametric regression and conditional distribution learning. Our approach simultaneously estimates a regression function and a conditional generator using a generative learning…
Random number generation is a key technology that is useful in a variety of ways. Random numbers are often used to generate keys for data encryption. Random numbers generated at a sufficiently long length can encrypt sensitive data and make…
One may consider three types of statistical inference: Bayesian, frequentist, and group invariance-based. The focus here is on the last method. We consider the Poisson and binomial distributions in detail to illustrate a group invariance…
Diffusion models are recent state-of-the-art methods for image generation and likelihood estimation. In this work, we generalize continuous-time diffusion models to arbitrary Riemannian manifolds and derive a variational framework for…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
In this study, we exhibit a number elementary strategies that might be at disposal in diverse computational applications in the GEANT4 simulations with the purpose of hemispherical particle sources. To further detail, we initially generate…
Although Poisson-Voronoi diagrams have interesting mathematical properties, there is still much to discover about the geometrical properties of its grains. Through simulations, many authors were able to obtain numerical approximations of…
In this paper, we aim to design and analyze distributed Bayesian estimation algorithms for sensor networks. The challenges we address are to (i) derive a distributed provably-correct algorithm in the functional space of probability…
We propose a new powerful family of tests of univariate normality. These tests are based on an initial value problem in the space of characteristic functions originating from the fixed point property of the normal distribution in the zero…
Motivated by the need, in some Bayesian likelihood free inference problems, of imputing a multivariate counting distribution based on its vector of means and variance-covariance matrix, we define a generic multivariate discrete…
A formalism is presented for analytically obtaining the probability density function, (P_{n}(s)), for the random distance (s) between two random points in an (n)-dimensional spherical object of radius (R). Our formalism allows (P_{n}(s)) to…
Results of numerical procedure of constructing confidence intervals for parameter of the Poisson distribution of signal events in the presence of background events with known value of parameter of Poisson distribution are presented. It is…