The function provides a method to approximate the weights of the mixture components, when the number of components is known as well as the degrees of freedom of each chi-square distribution in the mixture, and given a vector of simulated values from the target \(\bar{\chi}^2(V,C)\) distribution. Note that the estimation is based on (pseudo)-random Monte Carlo samples. For reproducible results, one should fix the seed of the (pseudo)-random number generator.
weightsChiBarSquare(df, V, dimsCone, orthan, control)a vector with the degrees of freedom of the chi-square components of the chi-bar-square distribution
a positive semi-definite matrix
a list with the dimensions of the cone C, expressed on the parameter space scale
a boolean specifying whether the cone is an orthan
(optional) a list of control options for the computation of the chi-bar-weights, containing
two elements: parallel a boolean indicating whether computation should be done in parallel (FALSE
by default), nb_cores the number of cores for parallel computing (if parallel=TRUE but no value is given
for nb_cores, it is set to number of detected cores minus 1), and M the Monte Carlo sample
size for the computation of the weights.
A list containing the estimated weights, the standard deviations of the estimated weights and the
random sample of M realizations from the chi-bar-square distribution