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# Fatigue Life (Birnbaum-Saunders) Distribution

## Parameters

- continuous shape parameter ()
- continuous scale parameter ()
- continuous location parameter ( yields the two-parameter Fatigue Life distribution)

## Two-Parameter Fatigue Life Distribution

### Cumulative Distribution Function

where is the PDF of the standard Normal distribution,  and 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("FatigueLife";Data;[Options]```1```) ``` Probability Density Function `FatigueLifePdf(x,alpha,beta,[gamma])` ``` =FatigueLifePdf(alpha;beta;[gamma]) =DistPdf("FatigueLife(alpha;beta;[gamma])";x) ``` Cumulative Distribution Function `FatigueLifeCdf(x,alpha,beta,[gamma])` ``` =FatigueLifeCdf(alpha;beta;[gamma]) =DistCdf("FatigueLife(alpha;beta;[gamma])";x) ``` Survival Function `FatigueLifeSurv(x,alpha,beta,[gamma])` ``` =DistSurv("FatigueLife(alpha;beta;[gamma])";x) ``` Hazard Function `FatigueLifeHaz(x,alpha,beta,[gamma])` ``` =FatigueLifeHaz(alpha;beta;[gamma]) =DistHaz("FatigueLife(alpha;beta;[gamma])";x) ``` Cumulative Hazard Function `FatigueLifeCumHaz(x,alpha,beta,[gamma])` ``` =DistCumHaz("FatigueLife(alpha;beta;[gamma])";x) ``` Inverse CDF (Quantile Function) `FatigueLifeInv(P,alpha,beta,[gamma])` ``` =FatigueLifeInv(alpha;beta;[gamma]) =DistInv("FatigueLife(alpha;beta;[gamma])";P) ``` Random Numbers `FatigueLifeRand(alpha,beta,[gamma])` ``` =FatigueLifeRand(alpha;beta;[gamma]) =DistRand("FatigueLife(alpha;beta;[gamma])") ``` Mode `FatigueLifeMode(alpha,beta,[gamma])` ``` =DistMode("FatigueLife(alpha;beta;[gamma])") ``` Mean `FatigueLifeMean(alpha,beta,[gamma])` ``` =FatigueLifeMean(alpha;beta;[gamma]) =DistMean("FatigueLife(alpha;beta;[gamma])") ``` Variance `FatigueLifeVar(alpha,beta,[gamma])` ``` =FatigueLifeVar(alpha;beta;[gamma]) =DistVar("FatigueLife(alpha;beta;[gamma])") ``` Standard Deviation `FatigueLifeStdev(alpha,beta,[gamma])` ``` =FatigueLifeStdev(alpha;beta;[gamma]) =DistStdev("FatigueLife(alpha;beta;[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).