Maximum likelihood estimates of the parameters are calculated by maximizing the likelihood function with respect to the parameters. The likelihood function describes, for each set of values of distribution parameters, the probability density for the observed data. The maximum likelihood estimates of the parameters make the observed data as likely as possible.
The Newton-Raphson1 algorithm is used to calculate maximum likelihood estimates of the parameters that define the distribution. The Newton-Raphson algorithm is a recursive method for computing the maximum of a function. The percentiles are calculated from that distribution. For computations, see Murray.1