Computing the distribution of a random variable via Gaussian quadrature rules

Using the technique of Gaussian quadrature rules, a new estimator is proposed for approximating the distribution of a random variable given only a finite number of its moments. The estimator is shown by numerous examples to be accurate on the tails of both continuous and discrete distributions. Efficient algorithms exist for computing the estimator from the first 2N moments of the random variable. A robust implementation of the estimator is presented, along with rules that provide additional protection against computer roundoff errors.