Related papers: The Multi-set Allocation Occupancy function and in…
General hypergeometric distribution (GHGD) definition: from a finite space $N$ containing $n$ elements, randomly select totally $T$ subsets $M_i$ (each contains $m_i$ elements, $1 \geq i \geq T$), what is the probability that exactly $x$…
General hypergeometric distribution (GHGD) describes the following distribution: from a finite space containing N elements, select T subsets with each subset contains M[i] (T-1 >= i >= 0) elements, what is the probability that exactly x…
This paper investigates the asymptotic behavior of the Multi-set Allocation Occupancy (MAO) distribution, which models the count vector $X=(X_{=0},\ldots,X_{=T})$ from $T$ independent rounds of sampling without replacement of size $m$ from…
The hypergeometric distribution is a popular distribution, whose properties have been extensively investigated. Generating functions of this distribution, such as the probability-generating function, the moment-generating function, and the…
The gamma difference distribution is defined as the difference of two gamma distributions, with in general different shape and rate parameters. Starting with knowledge of the corresponding characteristic function, a second order linear…
In this short note, explicit formulas are developed for the central and noncentral moments of the multivariate hypergeometric distribution. A numerical implementation is provided in Mathematica for fast evaluations. This work complements…
We give a bijection between a quotient space of the parameters and the space of moments for any $A$-hypergeometric distribution. An algorithmic method to compute the inverse image of the map is proposed utilizing the holonomic gradient…
Multivariate hypergeometric distribution arises frequently in elementary statistics and probability courses, for simultaneously studying the occurence law of specified events, when sampling without replacement from a finite population with…
We present the first general metric for attractor overlap (MAO) facilitating an unsupervised comparison of flow data sets. The starting point is two or more attractors, i.e., ensembles of states representing different operating conditions.…
In this note, we derive the closed form formulae for moments of Student's t-distribution in the one dimensional case as well as in higher dimensions through a unified probability framework. Interestingly, the closed form expressions for the…
A novel over-dispersed discrete distribution, namely the PoiTG distribution is derived by the convolution of a Poisson variate and an independently distributed transmuted geometric random variable. This distribution generalizes the…
The Wright function, which arises in the theory of the space-time fractional diffusion equation, is an interesting mathematical object which has diverse connections with other special and elementary functions. The Wright function provides a…
A new two-parameter discrete distribution, namely the PoiG distribution is derived by the convolution of a Poisson variate and an independently distributed geometric random variable. This distribution generalizes both the Poisson and…
As the unification of various models of ordered quantities, generalized order statistics act as a simplistic approach introduced in \cite{kamps1995concept}. In this present study, results pertaining to the expressions of marginal and joint…
We derive out naturally some important distributions such as high order normal distributions and high order exponent distributions and the Gamma distribution from a geometrical way. Further, we obtain the exact mean-values of integral form…
We develop a new approach for estimating the expected values of nonlinear functions applied to multivariate random variables with arbitrary distributions. Rather than assuming a particular distribution, we assume that we are only given the…
In this article, we show a new general linear independence criterion related to values of $G$-functions, including the linear independence of values at algebraic points of contiguous hypergeometric functions, which is not known before. Let…
The multivariate hypergeometric distribution describes sampling without replacement from a discrete population of elements divided into multiple categories. Addressing a gap in the literature, we tackle the challenge of estimating discrete…
We introduce an extension of the diagrammatic rules in random matrix theory and apply it to nonhermitean random matrix models using the 1/N approximation. A number of one- and two-point functions are evaluated on their holomorphic and…
Occupancy prediction infers fine-grained 3D geometry and semantics from camera images of the surrounding environment, making it a critical perception task for autonomous driving. Existing methods either adopt dense grids as scene…