Statmod: Probability calculations for the inverse Gaussian distribution

Abstract

The inverse Gaussian distribution (IGD) is a well known and often used probability distribution for which fully reliable numerical algorithms have not been available. We develop fast, reliable basic probability functions (dinvgauss, pinvgauss, qinvgauss and rinvgauss) for the IGD that work for all possible parameter values and which achieve close to full machine accuracy. The most challenging task is to compute quantiles for given cumulative probabilities and we develop a simple but elegant mathematical solution to this problem. We show that Newton's method for finding the quantiles of a IGD always converges monotonically when started from the mode of the distribution. Simple Taylor series expansions are used to improve accuracy on the log-scale. The IGD probability functions provide the same options and obey the same conventions as do probability functions provided in the stats package.