Generate <i>N</i>-Dimensional Normal Random Number via Wavelet Approach

Based on the wavelet image denoising method, a new approach is discussed for generating multi-dimensional normal random numbers in this paper. A thousand groups of multivariate random normal numbers are computed by this wavelet approach. According to Royston’s MVN test (Multivariate Normality test), the distributions of Royston’s test statistic and p-value are shown to illustrate multivariate normality in the boxplot figures. Moreover, based on the Jarque–Bera test, each row and column of the data are shown to illustrate normality in other boxplot figures, respectively. However, the distributions of average correlation and equivalent degrees of freedom are shown to illustrate possible correlation structure in the boxplot figures, compared to randn function and quantum random generator. Finally, the running times of this algorithm are also estimated, compared to the randn function and quantum random generator. The wavelet approach is faster than the randn function and quantum random generator in generating ultra-high-dimensional normal random numbers.