Related papers: Integer Partitions Probability Distributions
Consider a set of order statistics that arise from sorting samples from two different populations, each with their own, possibly different distribution function. The probability that these order statistics fall in disjoint, ordered…
Probabilistic programming is becoming increasingly popular thanks to its ability to specify problems with a certain degree of uncertainty. In this work, we focus on term rewriting, a well-known computational formalism. In particular, we…
We study the singularity probability of n*n random matrices with i.i.d. entries from highly biased discrete distributions. We obtain sharp non-asymptotic bounds for this probability and derive estimates on the least singular values. Our…
In the present work we show that the joint probability distribution of the eigenvalues can be expressed in terms of a differential operator acting on the distribution of some other matrix quantities. Those quantities might be the diagonal…
In this work we show that the prime distribution is deterministic. Indeed the set of prime numbers P can be expressed in terms of two subsets of N using three specific selection rules, acting on two sets of prime candidates. The prime…
We prove that the number of even parts and the number of times that parts are repeated have the same distribution over integer partitions with a fixed perimeter. This refines Straub's analog of Euler's Odd-Distinct partition theorem. We…
We show how to store good approximations of probability distributions in small space.
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical…
In 1882 J.J. Sylvester already proved, that the number of different ways to partition a positive integer into consecutive positive integers exactly equals the number of odd divisors of that integer (see [1]). We will now develop an…
An expression for the joint probability distribution of the principal curvatures at an arbitrary point in the ensemble of isosurfaces defined on isotropic Gaussian random fields on Rn is derived. The result is obtained by deriving symmetry…
Efficient and accurate estimation of multivariate empirical probability distributions is fundamental to the calculation of information-theoretic measures such as mutual information and transfer entropy. Common techniques include variations…
The partitions of the integers can be expressed exactly in an iterative and closed-form expression. This equation is derived from distributing the partitions of a number in a network that locates each partition in a unique and orderly…
The norm of an integer partition is defined as the product of its parts. This statistic was recently introduced by Schneider in connection to partition zeta functions. In this note, we use the method of moments to study the distribution of…
In the probabilistic approach to uncertainty management the input knowledge is usually represented by means of some probability distributions. In this paper we assume that the input knowledge is given by two discrete conditional probability…
The paper describes some probabilistic and combinatorial aspects of the nonlinear Fourier transform associated with the AKNS-ZS problems. In the first of the two main results, we show that a family of polytopes that appear in a power…
Quantization for probability distributions concerns the best approximation of a $d$-dimensional probability distribution $P$ by a discrete probability with a given number $n$ of supporting points. In this paper, we have considered a…
Let $\mathcal{P}=\{p_1,p_2,...\}$ be the set of all odd primes arranged in increasing order. A Goldbach partition of the even integer $2k>4$ is a way of writing it as a sum of two primes from $\mathcal{P}$ without regard to order. Let…
In this note, we represent integers in a type of factoradic notation. Rather than use the corresponding Lehmer code, we will view integers as permutations. Given a pair of integers n and k, we give a formula for n mod k in terms of the…
An "element-free" probability distribution is what remains of a probability distribution after we forget the elements to which the probabilities were assigned. These objects naturally arise in Bayesian statistics, in situations where…