Related papers: On the Maximum and Minimum of a Multivariate Poiss…
Given disjoint subsets $T_1,\ldots,T_m$ of "not too large" primes up to $x$, we establish that for a random integer $n$ drawn from $[1,x]$, the $m$-dimensional vector enumerating the number of prime factors of $n$ from $T_1,\ldots,T_m$…
Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm…
In this article, we discuss a bivariate distribution whose conditionals are univariate binomial distributions and the marginals are not binomial that exhibits negative correlation. Some useful structural properties of this distribution…
We consider the asymptotic distribution of a cell in a 2 x ... x 2 contingency table as the fixed marginal totals tend to infinity. The asymptotic order of the cell variance is derived and a useful diagnostic is given for determining…
A multivariate fractional Poisson process was recently defined in Beghin and Macci (2016) by considering a common independent random time change for a finite dimensional vector of independent (non-fractional) Poisson processes; moreover it…
Extended derivations regarding the cumulant-based formulation of higher-order fluorescence correlation spectroscopy (FCS) are presented. First, we review multivariate cumulants and their relation to photon counting distributions in single…
The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…
This article describes two Monte Carlo methods for calculating confidence intervals on cumulative density function (CDF) based multivariate normal quantiles that allows for controlling the tail regions of a multivariate distribution where…
Our interest is in the scaled joint distribution associated with $k$-increasing subsequences for random involutions with a prescribed number of fixed points. We proceed by specifying in terms of correlation functions the same distribution…
We study a new family of random variables, that each arise as the distribution of the maximum or minimum of a random number $N$ of i.i.d.~random variables $X_1,X_2,\ldots,X_N$, each distributed as a variable $X$ with support on $[0,1]$. The…
This paper studies fundamental aspects of modelling data using multivariate Watson distributions. Although these distributions are natural for modelling axially symmetric data (i.e., unit vectors where $\pm \x$ are equivalent), for…
Motivated by the fundamental problem of modeling the frequency of frequencies (FoF) distribution, this paper introduces the concept of a cluster structure to define a probability function that governs the joint distribution of a random…
Forward simulation-based uncertainty quantification that studies the distribution of quantities of interest (QoI) is a crucial component for computationally robust engineering design and prediction. There is a large body of literature…
We leverage neural networks as universal approximators of monotonic functions to build a parameterization of conditional cumulative distribution functions (CDFs). By the application of automatic differentiation with respect to response…
We show that for all $\psi$-mixing shifts distributions of the numbers of multiple recurrencies to shrinking cylindrical neighborhoods of all points are close either to Poisson or to compound Poisson distributions. We also describe…
This paper presents the probability distribution function (p.d.f.) and cumulative distribution function (c.d.f.) of the weighted sum of central independent chi-squared random variables with non-zero weighs based on a method using moment…
We propose a method for finding a cumulative distribution function (cdf) that minimizes the distance to a given cdf, while belonging to an ambiguity set constructed relative to another cdf and, possibly, incorporating soft information. Our…
We suggest a new hardcore Poisson-type distribution for Young diagrams with the row lengths from some finite list. A discrete variant of the time-ordered Mat\'{e}rn II process in 1D is employed. This approach is related to that based on the…
In the current paper, the estimation of the probability density function and the cumulative distribution function of the Topp-Leone distribution is considered. We derive the following estimators: maximum likelihood estimator, uniformly…
For independent random variables $(X_i)_{1\leq i\leq n}$, we consider the maximal correlation coefficient $R=R(\min_{i:1\leq i\leq m}X_i,\min_{j:\ell+1\leq j\leq n}X_j)$. If $X_1,X_2,\ldots,X_n$ are identically distributed with the same…