The information matrix of the bivariate extended skew-normal distribution

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.