Problem: Given a uniform random variable U, generate a random variable X having a prescribed distribution function F X) (⋅. We previously discussed the inversion method. While inversion is a very general method, it may be computationally expensive. In particular, computing 1 X F () − ⋅ may have to be implemented via a numerical root-finding method in many cases. Therefore, we will now describe ...

Abstract Order statistics arising from

asymptotically most powerful permutation (rank order) tests is offered for testing independence of two stochastic variates when the observable random variables correspond to a finite or countable set of contiguous cells having an underlying continuous distribution. The theory is illustrated by some examples.

This paper re-examines the density for sums of independent exponential, Erlang and gamma random variables. By using a divided difference perspective, provides unified approach to finding closed-form formulae such convolutions. In particular, perspective variates suggests new fractional calculus.

We congratulate the authors for the interesting paper. The reading has been really pleasant and instructive. We discuss briefly only some of the interesting results given in [6] with particular attention to evolution problems. The contribution of the results collected in the paper is useful in a more wide class of applications in many areas of applied mathematics. The paper under discussion is ...

The bivariate distribution with exponential conditionals (BEC) is introduced by Arnold and Strauss [Bivariate distributions with exponential conditionals, J. Amer. Statist. Assoc. 83 (1988) 522–527]. This work presents a simple and fast algorithm for simulating random variates from this density.

This paper provides an overview of the five most commonly used statistical techniques for improving the efficiency of stochastic simulations: control variates, common random numbers, importance sampling, conditional Monte Carlo, and stratification. The paper also describes a mathematical framework for discussion of efficiency issues that quantifies the trade-off between lower variance and highe...

The algorithm of Minh as in [Minh (1988)] was used to generate variates having a gamma distribution with shape parameter a>1 only. In this paper, a method, which is the improvement of the algorithm of Minh is introduced for the generation of independent random variables from a gamma distribution with all values of shape parameter and is compared with the method of Marsaglia and Tsang. By means ...

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...

In this paper we present the results of a rst empirical investigation on how the quality of non-uniform variates is innuenced by the underlying uniform RNG and the transformation method used. We use well known standard RNGs and transformation methods to the normal distribution as examples. We nd that except for transformed density rejection methods, which do not seem to introduce any additional...