  The inverse Gaussian distribution (IGD) is a well known and often used
probability distribution for which fully reliable numerical algorithms have not
been available. Our aim in this article is to develop software for this
distribution for the R programming environment. We develop fast, reliable basic
probability functions (dinvgauss, pinvgauss, qinvgauss and rinvgauss) 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 standard
R stats package. The IGD functions are part of the statmod package available
from the CRAN repository.
