Inverse Gaussian distribution

Inverse Gaussian

Probability density function
Parameters	$\lambda >0$ $\mu >0$
Support	$x\in (0,\infty )$
PDF	$[{\frac {\lambda }{2\pi x^{3}}}]^{\frac {1}{2}}\exp {\frac {-\lambda (x-\mu )^{2}}{2\mu ^{2}x}}$
Mean	$\mu$
Mode	$\mu [(1+{\frac {9\mu ^{2}}{4\lambda ^{2}}})^{\frac {1}{2}}-{\frac {3\mu }{2\lambda }}]$
Variance	${\frac {\mu ^{3}}{\lambda }}$
Skewness	$3({\frac {\mu }{\lambda }})^{\frac {1}{2}}$
Excess kurtosis	$3+{\frac {15\mu }{\lambda }}$

The probability density function of the inverse Gaussian distribution is given by

$f(x;\mu ,\sigma ,\lambda )=\left[{\frac {\lambda }{2\pi x^{3}}}\right]^{1/2}\exp {\frac {-\lambda (x-\mu )^{2}}{2\mu ^{2}x}}.$

The Wald distribution is a special case of the inverse Gaussian distribution with μ = λ = 1.

As λ tends to infinity, the inverse Gaussian distribution approaches a standard normal distribution.

External link

• Inverse Gaussian Distribution in Wolfram website.