Acronyms that contain the term Inverse Gaussian distribution 

Inverse Gaussian distribution

In probability theory, the inverse Gaussian distribution (also known as the Wald distribution) is a two-parameter family of continuous probability distributions with support on (0,∞). Its probability density function is given by f ( x ; μ , λ ) = λ 2 π x 3 exp ⁡ ( − λ ( x − μ ) 2 2 μ 2 x ) {\displaystyle f(x;\mu ,\lambda )={\sqrt {\frac {\lambda }{2\pi x^{3}}}}\exp {\biggl (}-{\frac {\lambda (x-\mu )^{2}}{2\mu ^{2}x}}{\biggr )}} for x > 0, where μ > 0 {\displaystyle \mu >0} is the mean and λ > 0 {\displaystyle \lambda >0} is the shape parameter.As λ tends to infinity, the inverse Gaussian distribution becomes more like a normal (Gaussian) distribution. The inverse Gaussian distribution has several properties analogous to a Gaussian distribution. The name can be misleading: it is an "inverse" only in that, while the Gaussian describes a Brownian motion's level at a fixed time, the inverse Gaussian describes the distribution of the time a Brownian motion with positive drift takes to reach a fixed positive level. Its cumulant generating function (logarithm of the characteristic function) is the inverse of the cumulant generating function of a Gaussian random variable. To indicate that a random variable X is inverse Gaussian-distributed with mean μ and shape parameter λ we write X ∼ IG ⁡ ( μ , λ ) {\displaystyle X\sim \operatorname {IG} (\mu ,\lambda )\,\!} .

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