Statistics, Department of

The R Journal
Date of this Version
8-2016
Document Type
Article
Citation
The R Journal (August 2016) 8(1); Editor: Michael Lawrence
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
Included in
Numerical Analysis and Scientific Computing Commons, Programming Languages and Compilers Commons
Comments
Copyright 2016, The R Foundation. Open access material. License: CC BY 3.0 Unported