Inverse Gaussian Distribution

Parameters

Domain

Three-Parameter Inverse Gaussian Distribution

Probability Density Function

Cumulative Distribution Function

Two-Parameter Inverse Gaussian Distribution

Probability Density Function

Cumulative Distribution Function

where is the Laplace Integral.

Worksheet and VBA Functions

The following worksheet and VBA functions are available for this distribution:

Description	VBA Functions	Worksheet Functions
Distribution Fitting	-	=DistFit("InvGaussian";Data;[Options]1)
Probability Density Function	InvGaussianPdf(x,lambda,mu,[gamma])	=InvGaussianPdf(lambda;mu;[gamma]) =DistPdf("InvGaussian(lambda;mu;[gamma])";x)
Cumulative Distribution Function	InvGaussianCdf(x,lambda,mu,[gamma])	=InvGaussianCdf(lambda;mu;[gamma]) =DistCdf("InvGaussian(lambda;mu;[gamma])";x)
Survival Function	InvGaussianSurv(x,lambda,mu,[gamma])	=DistSurv("InvGaussian(lambda;mu;[gamma])";x)
Hazard Function	InvGaussianHaz(x,lambda,mu,[gamma])	=InvGaussianHaz(lambda;mu;[gamma]) =DistHaz("InvGaussian(lambda;mu;[gamma])";x)
Cumulative Hazard Function	InvGaussianCumHaz(x,lambda,mu,[gamma])	=DistCumHaz("InvGaussian(lambda;mu;[gamma])";x)
Inverse CDF (Quantile Function)	InvGaussianInv(P,lambda,mu,[gamma])	=InvGaussianInv(lambda;mu;[gamma]) =DistInv("InvGaussian(lambda;mu;[gamma])";P)
Random Numbers	InvGaussianRand(lambda,mu,[gamma])	=InvGaussianRand(lambda;mu;[gamma]) =DistRand("InvGaussian(lambda;mu;[gamma])")
Mode	InvGaussianMode(lambda,mu,[gamma])	=DistMode("InvGaussian(lambda;mu;[gamma])")
Mean	InvGaussianMean(lambda,mu,[gamma])	=InvGaussianMean(lambda;mu;[gamma]) =DistMean("InvGaussian(lambda;mu;[gamma])")
Variance	InvGaussianVar(lambda,mu,[gamma])	=InvGaussianVar(lambda;mu;[gamma]) =DistVar("InvGaussian(lambda;mu;[gamma])")
Standard Deviation	InvGaussianStdev(lambda,mu,[gamma])	=InvGaussianStdev(lambda;mu;[gamma]) =DistStdev("InvGaussian(lambda;mu;[gamma])")
Skewness	InvGaussianSkew(lambda,mu,[gamma])	=DistSkew("InvGaussian(lambda;mu;[gamma])")
(Excess) Kurtosis	InvGaussianKurt(lambda,mu,[gamma])	=DistKurt("InvGaussian(lambda;mu;[gamma])")

1. The Options parameter is optional. Possible options: "gamma=value"  (example: "gamma=0")
2. The gamma parameter is optional (the default value is 0).