介观或动力学系统中随机电磁场的抽样分布
Sampling Distributions of Random Electromagnetic Fields in Mesoscopic or Dynamical Systems
摘要：
我们推导出一个理想的局部随机电磁场的采样概率密度函数（pdf），它的振幅和强度在准静态时变统计均匀或静态统计不均匀的电磁环境。当一个单一的空间或时间随机过程产生随机化的字段的字段统计和置信区间的估计的结果允许。相干和非相干检测技术的结果推导出，笛卡尔，平面和全矢量领域。我们表明，抽样pdf的函数形式取决于随机变量是否是维数（例如，采样的电场本身）或以无量纲标准化或归一化形式表示（例如，采样的电场除以其采样的标准偏差）。对于量纲量，电场，其幅度和强度表现出不同类型的贝塞尔$K$采样pdf，当$ν$相对较小时，其与渐近高斯正态和$χ^{(2)}_{2p}$系综pdf显著不同。相比之下，对于相应的标准化量，获得了学生$t$、Fisher-Snedecor $F$和root-$F$采样pdf，其表现出比可比的Bessel $K$ pdf更重的尾部。从经典的小样本理论的无量纲量的统计不确定性被高估相比，有量纲的量。从去规范化与去标准化所产生的采样PDF的差异。
英文摘要：
We derive the sampling probability density function (pdf) of an ideal localized random electromagnetic field, its amplitude and intensity in an electromagnetic environment that is quasi-statically time-varying statistically homogeneous or static statistically inhomogeneous. The results allow for the estimation of field statistics and confidence intervals when a single spatial or temporal stochastic process produces randomization of the field. Results for both coherent and incoherent detection techniques are derived, for Cartesian, planar and full-vectorial fields. We show that the functional form of the sampling pdf depends on whether the random variable is dimensioned (e.g., the sampled electric field proper) or is expressed in dimensionless standardized or normalized form (e.g., the sampled electric field divided by its sampled standard deviation). For dimensioned quantities, the electric field, its amplitude and intensity exhibit different types of Bessel $K$ sampling pdfs, which differ significantly from the asymptotic Gauss normal and $χ^{(2)}_{2p}$ ensemble pdfs when $ν$ is relatively small. By contrast, for the corresponding standardized quantities, Student $t$, Fisher-Snedecor $F$ and root-$F$ sampling pdfs are obtained that exhibit heavier tails than comparable Bessel $K$ pdfs. Statistical uncertainties obtained from classical small-sample theory for dimensionless quantities are shown to be overestimated compared to dimensioned quantities. Differences in the sampling pdfs arising from de-normalization versus de-standardization are obtained.
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