A simple generalization of the Box–Muller method for obtaining a pair of correlated standard normal variables

In the simple and widely used method of Box–Muller [G. Box and M. Muller, A note on the generation of random normal deviates, Ann. Math. Statist. 29 (1958), pp. 610–611], from a pair of uniform and independent random variables in (0,1), a pair of standard and independent normal variables is obtained. In this article, we present a very simple and elegant generalization of this method to obtain a pair of correlated standard normal variables with a given coefficient of correlation. This generalized method, which is computationally very easy, is interpreted in geometric terms, considering a translation of the uniform interval (0,1) and a rotation of a defined angle, both related to the coefficient of correlation. Some numerical results are simulated and statistically analysed, proving that the generalization is extremely simple and powerful.     

On Box–Muller Transformation and Simulation of Normal Record Data

Record data are commonly encountered in many fields such as sports, geography, finance, and reliability. In this article, we use the well-known Box–Muller transformation to develop an efficient method of simulating record data from the normal distribution. Another method based on exponential records is also discussed. Then, the performance of these algorithms is compared with some standard simulation methods.     

白斑综合征病毒感染褶皱臂尾轮虫的初步研究

对褶皱臂尾轮虫进行白斑综合征病毒(WSSV)攻毒,然后将攻毒前后的轮虫进行PCR及核酸探针斑点杂交检测.结果表明,攻毒后的褶皱臂尾轮虫呈WSSV阴性,说明褶皱臂尾轮虫可能不传播WSSV.