Related papers: Properties and conjectures regarding discrete rene…
We give a decomposition of the posterior predictive variance using the law of total variance and conditioning on a finite dimensional discrete random variable. This random variable summarizes various features of modeling that are used to…
In this survey, we discuss some basic problems concerning random matrices with discrete distributions. Several new results, tools and conjectures will be presented.
Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…
Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…
We derive basic properties of minimal extensions of local rings and their restrictions to subrings. Some applications are included to subrings of truncated polynomial rings.
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…
The aims of this paper are twofold. Firstly, we derive some probabilistic representation for the constant which appears in the one-dimensional case of Kesten's renewal theorem. Secondly, we estimate the tail of some related random variable…
Motivated by a question of van der Poorten about the existence of infinite chain of prime numbers (with respect to some base), in this paper we advance the study of sequences of consecutive polynomials whose coefficients are chosen…
In this note we put forward a conjecture on the average optimal length for bipartite matching with a finite number of elements where the different lengths are independent one from the others and have an exponential distribution.
This paper considers estimation of a univariate density from an individual numerical sequence. It is assumed that (i) the limiting relative frequencies of the numerical sequence are governed by an unknown density, and (ii) there is a known…
In an earlier paper, we discussed the probability that the determinant of a matrix undergoes the least change upon perturbation of one of its elements, provided that most or all of the elements of the matrix are chosen at random and that…
In this paper, we study a class of functions defined recursively on the set of natural numbers in terms of the greatest common divisor algorithm of two numbers and requiring a minimality condition. These functions are permutations, products…
We introduce the notion of a bivariate random discrete copula on an equidistant mesh and explore its stochastic properties. A random discrete copula is a discrete random field, hence, its value at a given point on the mesh is a random…
Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal…
This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we present algorithms to compute more precise…
We study an infinite class of sequences of sparse polynomials that have binomial coefficients both as exponents and as coefficients. This generalizes a sequence of sparse polynomials which arises in a natural way as graph theoretic…
In this paper, we study a multidimensional risk model with a common renewal process and in the presence of a constant interest force. The claim sizes are independent and identically distributed random vectors, with the distribution of…
Current discrete randomness and information conservation inequalities are over total recursive functions, i.e. restricted to deterministic processing. This restriction implies that an algorithm can break algorithmic randomness conservation…
We study approximation in the unit interval by rational numbers whose numerators are selected randomly with certain probabilities. Previous work showed that an analogue of Khintchine's Theorem holds in a similar random model and raised the…
Assuming a $q$-variant of the prime $k$-tuple conjecture uniformly, we compute mixed moments of the number of primes in disjoint short intervals and progressions, respectively. This involves estimating the mean of singular series along…