First, likelihood ratio statistics for checking the hypothesis of equal variances of two-dimensional Gaussian vectors are derived both under the standard $\left (\sigma ^{2}_{1},\sigma ^{2}_{2},\varrho \right)$ -parametrization and under the geometric (a,b,α)-parametrization where a 2 and b 2 are the variances of the principle components and α is an angle of rotation. Then, the likelihood ratio statistics for checking the hypothesis of equal scaling parameters of principle components of p-power exponentially distributed two-dimensional vectors are considered both under independence and under rotational or correlation type dependence. Moreover, the role semi-inner products play when establishing various likelihood equations is demonstrated. Finally, the dependent p-generalized polar method and the dependent p-generalized rejection-acceptance method for simulating star-shaped distributed vectors are presented.

中文翻译：

---

相关p-广义椭圆轮廓分布及其以外的统计推理

首先，根据标准$ \ left（\ sigma ^ {2} _ {1}，\ sigma ^ {2} _ {2}，得出用于检查二维高斯矢量等方差假设的似然比统计量， \ varrho \ right）$-参数化和几何（a，b，α）参数化，其中a 2和b 2是主成分的方差，α是旋转角度。然后，在独立性和旋转或相关类型相关性的条件下，考虑似然比统计数据，以检查p幂指数分布的二维矢量的主成分的相等缩放参数的假设。此外，还演示了半内部产品在建立各种似然方程时所起的作用。最后，