Monte Carlo techniques are often the only practical way to evaluate difficult integrals or to sample random variables governed by complicated probability density functions. Here we describe an assortment of methods for sampling some commonly occurring probability density functions. Most Monte Carlo sampling or integration techniques assume a " random number generator, " which generates uniform ...

Monte Carlo techniques are often the only practical way to evaluate difficult integrals or to sample random variables governed by complicated probability density functions. Here we describe an assortment of methods for sampling some commonly occurring probability density functions. Most Monte Carlo sampling or integration techniques assume a " random number generator, " which generates uniform ...

Pseudorandom number generators are required for many computational tasks, such as stochastic modelling and simulation. This paper investigates the serial CPU and parallel GPU implementation of a Linear Congruential Generator based on the binary representation of the normal number α2,3. We adapted two methods of modular reduction which allowed us to perform most operations in 64-bit integer arit...

Cryptographically secure pseudorandom number generators known so far suffer from the handicap of being inefficient; the most efficient ones can generate only one bit on each modular multiplication (n2 steps). Hum, Blum and Shub ask the open problem of outputting even two bits securely. We state a simple condition, the XORCondition. and show that any generator satisfying this condition can outpu...

The Scalable Parallel Random Number Generators (SPRNG) library is widely used to generate random numbers in Monte Carlo simulations due to the good statistical properties of both its serial and parallel random number streams. In this paper, we suggest an efficient hardware architecture for the Parallel Additive Lagged-Fibonacci Generator (PALFG) provided by the SPRNG library. This design has be...

Topological data analysis (TDA) studies the shape patterns of data. Persistent homology is a widely used method in TDA that summarizes homological features at multiple scales and stores them persistence diagrams (PDs). In this paper, we propose random diagram generator (RPDG) generates sequence PDs from ones produced by RPDG underpinned model based on pairwise interacting point processes revers...