Related papers: Telescoping Sums, Permutations, and First Occurren…
We investigate the problem of the distribution of sums of functions of prime numbers located on an arithmetic progression. This problem is closely related to the problem of the distribution of prime numbers on an arithmetic progression.…
Urn models play an important role to express various basic ideas in probability theory. Here we extend this urn model with tubes. An urn contains coloured balls, which can be drawn with probabilities proportional to the numbers of balls of…
We present efficient methods for calculating linear recurrences of hypergeometric double sums and, more generally, of multiple sums. In particular, we supplement this approach with the algorithmic theory of contiguous relations, which…
Diffusion models have excellent capacity to model complex distributions of natural data, which has made them a popular and effective choice for posterior sampling in imaging inverse problems. Existing methods can incorporate any measurement…
In this paper, we focus on the enumeration of permutations by number of cyclic occurrence of peaks and valleys. We find several recurrence relations involving the number of permutations with a prescribed number of cyclic peaks, cyclic…
We adopt a physically motivated empirical approach to the characterisation of the distributions of twin and triplet primes within the set of primes, rather than in the set of all natural numbers. Remarkably, the occurrences of twins or…
Triangular distributions are a well-known class of distributions that are often used as an elementary example of a probability model. Maximum likelihood estimation of the mode parameter of the triangular distribution over the unit interval…
We study finite $l$-colourable structures with an underlying pregeometry. The probability measure that is used corresponds to a process of generating such structures (with a given underlying pregeometry) by which colours are first randomly…
The study of the optical transmission matrix (TM) of a sample reveals important statistics of light transport through it. The accuracy of the statistics depends strongly on the orthogonality and completeness of the basis in which the TM is…
Uniform probability distributions on $\ell_p$ balls and spheres have been studied extensively and are known to behave like product measures in high dimensions. In this note we consider the uniform distribution on the intersection of a…
The asymptotic behavior of the tail probabilities for the first hitting times of the Bessel process with arbitrary index is shown without using the explicit expressions for the distribution function obtained in the authors' previous works.
Philosophers now seem to agree that frequentism is an untenable strategy to explain the meaning of probabilities. Nevertheless, I want to revive frequentism, and I will do so by grounding probabilities on typicality in the same way as the…
We consider two orthogonal points of view on finite permutations, seen as pairs of linear orders (corresponding to the usual one line representation of permutations as words) or seen as bijections (corresponding to the algebraic point of…
The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability…
It is known that large deviations of sums of subexponential random variables are most likely realised by deviations of a single random variable. In this article we give a detailed picture of how subexponential random variables are…
Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic…
This paper examines the classical matching distribution arising in the "problem of coincidences". We generalise the classical matching distribution with a preliminary round of allocation where items are correctly matched with some fixed…
Karlin and Altschul in their statistical analysis for multiple high-scoring segments in molecular sequences introduced a distribution function which gives the probability there are at least r distinct and consistently ordered segment pairs…
Lexicographic or first choice constructions of geometric objects sometimes lead to amazingly good results. Usually it is difficult to determine the precise identity of these geometries. Here we find infinitely many cases where the…
A new class of random spatial tessellations is introduced -- the so-called column tessellations of three-dimensional space. The construction is based on a stationary planar tessellation. Each cell of the spatial tessellation is a prism…