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In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
We study the statistical properties of the generation of random graphs according the configuration model, where one assigns randomly degrees to nodes. This model is often used, e.g., for the scale-free degree distribution ~d^gamma. For the…
The Gamma distribution is well-known and widely used in many signal processing and communications applications. In this letter, a simple and extremely efficient accept/reject algorithm is introduced for the generation of independent random…
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 method for generating random $U(1)$ variables with Boltzmann distribution is presented. It is based on the rejection method with transformation of variables. High efficiency is achieved for all range of temparatures or coupling…
For two vast families of mixture distributions and a given prior, we provide unified representations of posterior and predictive distributions. Model applications presented include bivariate mixtures of Gamma distributions labelled as…
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…
This article introduces an algorithm to draw random discrete uniform variables within a given range of size n from a source of random bits. The algorithm aims to be simple to implement and optimal both with regards to the amount of random…
In this paper, we introduce a new probability distribution, the Lasso distribution. We derive several fundamental properties of the distribution, including closed-form expressions for its moments and moment-generating function.…
Markov-chain Monte Carlo algorithms rely on trial moves that are either rejected or accepted based on certain criteria. Here, we provide an efficient algorithm to generate random rotation matrices in four dimensions (4D) covering an…
A novel approach towards construction of absolutely continuous distributions over the unit interval is proposed. Considering two absolutely continuous random variables with positive support, this method conditions on their convolution to…
By using the matrix formulation of the two-step approach to distributions of patterns in random sequences, recurrence and explicit formulas for the generating functions of successions in random permutations of arbitrary multisets are…
We survey some recent progress on rigorously establishing the universality of various spectral statistics of Wigner random matrix ensembles, focusing in particular on the Four Moment Theorem and its applications.
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
Random numbers are widely used for information security, cryptography, stochastic modeling, and quantum simulations. Key technical challenges for physical random number generation are speed and scalability. We demonstrate a method for…
A procedure for generating random variates from a relativistic Maxwellian distribution with arbitrary temperature and drift velocity is presented. The algorithm is based on the rejection method and can be used to initialize particle…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
In this paper, we propose a discrete circular distribution obtained by extending the wrapped Poisson distribution. This new distribution, the Invariant Wrapped Poisson (IWP), enjoys numerous advantages: simple tractable density,…
New results on uniform convergence in probability for the most general classes of wavelet expansions of stationary Gaussian random processes are given.
Matrix multivariate Pearson type II-Riesz distribution is defined and some of its properties are studied. In particular, the associated matrix multivariate beta distribution type I is derived. Also the singular values and eigenvalues…