The transformed rejection method uses inversion to sample from the dominating density of a rejection algorithm. But in contrast to the usual method it is enough to know the inverse distribution function F^(-1)(x) of the dominating density. This idea can be applied to various continuous (e.g. normal, Cauchy and exponential) and discrete (e.g. binomial and Poisson) distributions with high acceptance probabilities. The resulting algorithms are short, simple and fast. Even more important is the fact that the quality of the method when used in combination with a linear congruential uniform generator is high compared with the quality of the ratio of uniforms method. In addition transformed rejection can be easily employed for correlation induction. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

The quality of non-uniform random numbers is not only influenced by the quality of the uniform generator that is used but also by the transformation method applied to the uniform random numbers. This differences in quality between ``exact" methods were almost entirely neglected in literature. So we compare the behaviour of four different transformation methods when combined with a linear congruential uniform generator (LCG). Heuristic considerations, the computation of two measures of approximation and a statistical test show that the inversion method performs best. Among the others rejection, when combined with a LCG with small multiplier, and ratio of uniforms perform worse. Their use could slightly change the results of some simulation studies. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

The transformed rejection method, a combination of the inversion and the rejection method, which is used to generate non-uniform random numbers from a variety of continuous distributions can be applied to discrete distributions as well. For the Poisson distribution a short and simple algorithm is obtained which is well suited for large values of the Poisson parameter $\mu$, even when $\mu$ may vary from call to call. The average number of uniform deviates required is lower than for any of the known uniformly fast algorithms. Timings for a C implementation show that the algorithm needs only half of the code but is - for $\mu$ not too small - at least as fast as the current state-of-the-art algorithms. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

The one-dimensional distribution of pseudo-random numbers generated by the ratio of uniforms methods using linear congruential generators (LCGs) as the source of uniform random numbers is investigated in this paper. Due to the two-dimensional lattice structure of LCGs there is always a comparable large gap without a point in the one-dimensional distribution of any ratio of uniforms method. Lower bounds for these probabilities only depending on the modulus and the Beyer quotient of the LCG are proved for the case that the Cauchy the normal or the exponential distribution are generated. These bounds justify the recommendation not to use the ratio of uniforms method combined with LCGs. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

The transformed rejection method, a combination of inversion and rejection, which can be applied to various continuous distributions, is well suited to generate binomial random variates as well. The resulting algorithms are simple and fast, and need only a short set-up. Among the many possible variants two algorithms are described and tested: BTRS a short but nevertheless fast rejection algorithm and BTRD which is more complicated as the idea of decomposition is utilized. For BTRD the average number of uniforms required to return one binomial deviate lies between 2.5 and 1.4 which is considerably lower than for any of the known uniformly fast algorithms. Timings for a C-implementation show that for the case that the parameters of the binomial distribution vary from call to call BTRD is faster than the current state of the art algorithms. Depending on the computer, the speed of the uniform generator used and the binomial parameters the savings are between 5 and 40 percent. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

Up to now all known efficient portable implementations of linear congruential random number generators with modulus 2^(31)-1 are working only with multipliers which are small compared with the modulus. We show that for non-uniform distributions, the rejection method may generate random numbers of bad quality if combined with a linear congruential generator with small multiplier. Therefore a method is described that works for any multiplier smaller than 2^(30). It uses the decomposition of multiplier and seed in high order and low order bits to compute the upper and the lower half of the product. The sum of the two halfs gives the product of multiplier and seed modulo 2^(31)-1. Coded in ANSI-C and FORTRAN77 the method results in a portable implementation of the linear congruential generator that is as fast or faster than other portable methods. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing