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# Inverse Gaussian Distribution

## Parameters

- continuous parameter ()
- continuous parameter ()
- continuous location parameter ( yields the two-parameter Inverse Gaussian distribution)

## Two-Parameter Inverse Gaussian Distribution

### 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).