For the extended skew-normal distribution, which represents an extension of the normal (or Gaussian) distribution, we focus on the properties of the log-likelihood function and derived quantities in the the bivariate case. Specifically, we derive explicit expressions for the score function and the information matrix, in the observed and the expected form; these do not appear to have been examined before in the literature. Corresponding computing code in R language is provided, which implements the formal expressions.

翻译：对于作为正态（高斯）分布扩展形式的扩展偏正态分布，我们聚焦于双变量情形下对数似然函数及其导出量的性质。具体而言，我们推导了得分函数和信息矩阵的显式表达式，涵盖观测形式与期望形式；这些内容在文献中尚未见报道。文中提供了相应的R语言计算代码，用于实现上述形式化表达式。