Fatigue Life (Birnbaum-Saunders) Distribution

Parameters

Domain

Three-Parameter Fatigue Life Distribution

Probability Density Function

Cumulative Distribution Function

Two-Parameter Fatigue Life Distribution

Probability Density Function

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).