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# Levy Distribution

## Parameters

- continuous scale parameter ()
- continuous location parameter ( yields the one-parameter Levy distribution)

## One-Parameter Levy 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("Levy";Data;[Options]```1```) ``` Probability Density Function `LevyPdf(x,sigma,[gamma])` ``` =LevyPdf(sigma;[gamma]) =DistPdf("Levy(sigma;[gamma])";x) ``` Cumulative Distribution Function `LevyCdf(x,sigma,[gamma])` ``` =LevyCdf(sigma;[gamma]) =DistCdf("Levy(sigma;[gamma])";x) ``` Survival Function `LevySurv(x,sigma,[gamma])` ``` =DistSurv("Levy(sigma;[gamma])";x) ``` Hazard Function `LevyHaz(x,sigma,[gamma])` ``` =LevyHaz(sigma;[gamma]) =DistHaz("Levy(sigma;[gamma])";x) ``` Cumulative Hazard Function `LevyCumHaz(x,sigma,[gamma])` ``` =DistCumHaz("Levy(sigma;[gamma])";x) ``` Inverse CDF (Quantile Function) `LevyInv(P,sigma,[gamma])` ``` =LevyInv(sigma;[gamma]) =DistInv("Levy(sigma;[gamma])";P) ``` Random Numbers `LevyRand(sigma,[gamma])` ``` =LevyRand(sigma;[gamma]) =DistRand("Levy(sigma;[gamma])") ``` Mode `LevyMode(sigma,[gamma])` ``` =DistMode("Levy(sigma;[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).