Related papers: Generating pseudo-random discrete probability dist…
The goal of this study is to introduce a unified computational framework for simulating random iteration equations (RIE), understood as iteration equations containing random variables. The novelty of this work is that full probability…
In meta analysis, multiple hypothesis testing and many other methods, p-values are utilized as inputs and assumed to be uniformly distributed over the unit interval under the null hypotheses. If data used to generate p-values have discrete…
Pseudorandmness plays an important role in number theory, complexity theory and cryptography. Our aim is to use models of arithmetic to explain pseudorandomness by randomness. To this end we construct a set of models $\cal M$, a common…
The inverse Gaussian distribution (IGD) is a well known and often used probability distribution for which fully reliable numerical algorithms have not been available. Our aim in this article is to develop software for this distribution for…
The concept of randomness plays an important role in many disciplines. On one hand, the question of whether random processes exist is fundamental for our understanding of nature. On the other hand, randomness is a resource for cryptography,…
In this paper we examine quantile-stratified samples from a known univariate probability distribution, with stratification occurring over a partition of the quantile regions in the distribution. We examine some general properties of this…
Given a matrix $A\in \mathrm{GL}_d(\mathbb{Z})$. We study the pseudorandomness of vectors $\mathbf{u}_n$ generated by a linear recurrent relation of the form $$ \mathbf{u}_{n+1} \equiv A \mathbf{u}_n \pmod {p^t}, \qquad n = 0, 1, \ldots, $$…
Harnessing quantum processes is an efficient method to generate truly indeterministic random numbers, which are of fundamental importance for cryptographic protocols, security applications or Monte-Carlo simulations. Recently, quantum…
In this paper we study von Neumann un-biasing normalisation for ideal and real quantum random number generators, operating on finite strings or infinite bit sequences. In the ideal cases one can obtain the desired un-biasing. This relies…
Random numbers are used in a wide range of sciences. In many applications, generating unpredictable private random numbers is indispensable. Device-independent quantum random number generation is a framework that makes use of the intrinsic…
Inverse transform sampling is an exceptionally general method to generate non-uniform-distributed random numbers, but can be rather unstable when simulating extremely truncated distributions. Many famous probability models share a property…
The paper study counter-dependent pseudorandom number generators based on $m$-variate ($m>1$) ergodic mappings of the space of 2-adic integers $\Z_2$. The sequence of internal states of these generators is defined by the recurrence law…
Measurements of quantum systems can be used to generate classical data that is truly unpredictable for every observer. However, this true randomness needs to be discriminated from randomness due to ignorance or lack of control of the…
A new method for parallel generation of $q$-valued pseudorandom sequence based on the presentation of systems generating logical formulae by means of arithmetic polynomials is proposed. Fragment consisting of $k$-elements of $q$-valued…
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…
Differential Privacy (DP) relies on random numbers to preserve privacy, typically utilising Pseudorandom Number Generators (PRNGs) as a source of randomness. In order to allow for consistent reproducibility, testing and bug-fixing in DP…
Quantum key distribution (QKD) offers a way for establishing information-theoretically secure communications. An important part of QKD technology is a high-quality random number generator (RNG) for quantum states preparation and for…
Emergence of stochastic simulations as an extensively used computational tool for scientific purposes intensified the need for more accurate ways of generating sufficiently long sequences of uncorrelated random numbers. Even though several…
This paper proposes an algorithm to generate random numbers from any member of the truncated multivariate elliptical family of distributions with a strictly decreasing density generating function. Based on Neal (2003) and Ho et al. (2012),…
We consider the discrete three dimensional scan statistics. Viewed as the maximum of an 1-dependent stationary r.v.'s sequence, we provide approximations and error bounds for the probability distribution of the three dimensional scan…