论文标题
多高斯随机变量
Multi-Gaussian random variables
论文作者
论文摘要
还引入了以形状参数m> 0为特征的多高斯（MG）随机变量的经典高斯随机变量的概括，除了平均值和标准偏差之外。 MG家族成员的概率密度函数是具有适当选择的高度和宽度的高斯函数的交替系列。特别是，对于M的整数值，该系列具有有限数量的术语，并导致扁平的曲线，同时将M = 1的经典高斯密度降低到经典的高斯密度。对于非全能器，M的正值在实际问题中可以忽略了一系列无限的无限无限型高斯函数。尽管对于所有m> 1，Mg PDF都符合剖面，但对于0 <m <1，它导致了凹陷的轮廓。此外，获得了MG随机变量的多元扩展，并引入了log-multi-gaussian（LMG）随机变量。
A generalization of the classic Gaussian random variable to the family of Multi- Gaussian (MG) random variables characterized by shape parameter M > 0, in addition to the mean and the standard deviation, is introduced. The probability density function of the MG family members is the alternating series of the Gaussian functions with the suitably chosen heights and widths. In particular, for the integer values of M the series has finite number of terms and leads to flattened profiles, while reducing to classic Gaussian density for M = 1. For non-integer, positive values of M a convergent infinite series of Gaussian functions is obtained that can be truncated in practical problems. While for all M > 1 the MG PDF has attened profiles, for 0 < M < 1 it leads to cusped profiles. Moreover, the multivariate extension of the MG random variable is obtained and the Log-Multi-Gaussian (LMG) random variable is introduced.
