generate_skewed_t generates n random observations from the univariate skewed t-distribution
described in Hansen (1994) using the acceptance-rejection sampling method.
generate_skewed_t(n, nu, lambda, bc_M)A numeric vector of length n containing random observations from the skewed t-distribution with
parameters nu and lambda.
An integer specifying the number of random observations to generate. Must be a positive integer.
A numeric scalar specifying the degrees of freedom parameter for the skewed t-distribution. Must be greater than 2.
A numeric scalar specifying the skewness parameter for the skewed t-distribution. Must be between \(-1\) and \(1\).
An optional numeric scalar specifying the bounding constant \(M\) used in the acceptance-rejection algorithm.
If not provided, it is computed using bounding_const_M with the given nu and lambda.
The function implements the acceptance-rejection algorithm to generate random samples from the skewed t-distribution.
The proposal distribution used is a standard t-distribution with degrees of freedom proposal_nu, which is set to \(3\)
when nu > 3 to ensure heavier tails and accommodate the skewness of the target distribution.
If bounding_const_M is not provided, it is calculated using the bounding_const_M function. It is important that
the same proposal distribution is used in both the computation of bounding_const_M and the acceptance-rejection sampling
algorithm to ensure correctness.
Hansen B.E. 1994. Autoregressive Conditional Density estimation. Journal of Econometrics, 35:3, 705-730.