bounding_const_M calculates the bounding constant \(M\) used in the acceptance-rejection sampling algorithm
for the univariate skewed t-distribution described in Hansen (1994)
bounding_const_M(nu, lambda)Returns a numeric scalar representing the estimated bounding constant \(M\) to be used in the acceptance-rejection sampling algorithm.
the degrees of freedom parameter value, a numeric scalar strictly larger than two.
the skewness parameter value, a numeric scalar strictly between -1 and 1.
The function computes the bounding constant \(M\) required for the acceptance-rejection sampling method by evaluating
the ratio of the skewed t-density (skewed_t_dens) to the standard t-density (stand_t_dens)
over a grid of \(y\) values ranging from \(-10\) to \(10\). To improve the efficiency of the sampling algorithm, the degrees
of freedom parameter for the proposal distribution is set to the minimum of nu and \(3\), ensuring heavier tails in the
proposal distribution when nu is large. A safety margin of 10% is added to the maximum ratio to account for numerical
inaccuracies and ensure that the inequality \(f(y) \leq M \cdot q(y)\) holds over the entire support.
Hansen B.E. 1994. Autoregressive Conditional Density estimation. Journal of Econometrics, 35:3, 705-730.