Zusammenfassung Generating Beta Variates Via Patchwork Rejection. A new algorithm for sampling from beta(p; q) distributions with parameters p ? 1, q ? 1 is developed. It is based on a method by Minh [9] which improves acceptance--rejection sampling in the main part of the distributions. Additionally, transformed uniform deviates can often be accepted immediately, so that much fewer than two uniforms are needed for one beta variate, on the average. The remaining tests for acceptance are enhanced by 'squeezes'. Experiments covering a wide range of pairs (p; q) showed improvements in speed over competing algorithms in most cases.

for any errors or inaccuracies that may appear in this document or any software that may be provided in association with this document. This document and the software described in it are furnished under license and may only be used or copied in accordance with the terms of the license. No license, express or implied, by estoppel or otherwise, to any intellectual property

The information in this document is subject to change without notice and Intel Corporation assumes no responsibility or liability for any errors or inaccuracies that may appear in this document or any software that may be provided in association with this document. This document and the software described in it are furnished under license and may only be used or copied in accordance with the terms of the license. No license, express or implied, by estoppel or otherwise, to any intellectual property rights is granted by this document. The information in this document is provided in connection with Intel products and should not be construed as a commitment by Intel Corporation.

umbers. (b) Return the the a smallest number as BT(a# b). 3. If a and b are less than one: (a) Generate two uniform U(0,1) random numbers u (b) Let x = u and y = u . If (x + y) ? 1, go back to the previous step. Otherwise, return x=(x + y) as BT(a# b). 4. If a and b are greater than 1: Use rejection Binomial Distribution ffl The number of successes x in a sequence of n Bernoulli trials has a binomial distribution. ffl Characteristics: p = Probability of success in a trial, 0 ! p ! 1. n = Number of trials# n must be a positive integer. 2. Range: x = 0# 1# : : : # n B B B B C C C C n;x 4. Mean: np 5. Variance: np(1 ; p) successes 1. The number of processors that are up in a multiprocessor system. 2. The number of packets that reach the destination without loss. 3. The number of bits in a packet that are not affected by noise. 4. The number of items in a batch that have certain characteristics. ffl Variance ! Mean ) Binomial Variance ? Mean ) Negative Binomial Va

This paper proposes an improved gamma random generator. In the past, a lot of gamma random number generators have been proposed, and depending on a shape parameter (say, alpha) they are roughly classified into two cases: (i) alpha lies on the interval (0,1) and (ii) alpha is greater than 1, where alpha=1 can be included in either case. In addition, Cheng and Feast (1980) extended the gamma random number generator in the case where alpha is greater than 1/n, where n denotes an arbitrary positive number. Taking n as a decreasing function of alpha, in this paper we propose a simple gamma random number generator with shape parameter alpha greater than zero. The proposed algorithm is very simple and shows quite good performance.

Abstract not found