Inverse Gaussian Distribution

R2026b

Definition

The inverse Gaussian distribution has the density function

$$\sqrt{\frac{\lambda }{2\pi x^3}}\exp \left\{-\frac{\lambda }{2{\mu }^{2}x}{\left(x-\mu \right)}^2\right\}$$

Background

Also known as the Wald distribution, the inverse Gaussian is used to model nonnegative positively skewed data. The distribution originated in the theory of Brownian motion, but has been used to model diverse phenomena. Inverse Gaussian distributions have many similarities to standard Gaussian (normal) distributions, which lead to applications in inferential statistics.

Parameters

The inverse Gaussian distribution uses the following parameters.

Parameter	Description	Support
μ	Scale parameter	$$\mu >0$$
λ	Shape parameter	$$\lambda >0$$

To estimate distribution parameters, use mle or the Distribution Fitter app.