Log-Logistic Distribution

Parameters

Domain

Three-Parameter Log-Logistic Distribution

Probability Density Function

Cumulative Distribution Function

Two-Parameter Log-Logistic Distribution

Probability Density Function

Cumulative Distribution Function

Worksheet and VBA Functions

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

Description	VBA Functions	Worksheet Functions
Distribution Fitting	-	=DistFit("LogLogistic";Data;[Options]1)
Probability Density Function	LogLogisticPdf(x,alpha,beta,[gamma])	=LogLogisticPdf(alpha;beta;[gamma]) =DistPdf("LogLogistic(alpha;beta;[gamma])";x)
Cumulative Distribution Function	LogLogisticCdf(x,alpha,beta,[gamma])	=LogLogisticCdf(alpha;beta;[gamma]) =DistCdf("LogLogistic(alpha;beta;[gamma])";x)
Survival Function	LogLogisticSurv(x,alpha,beta,[gamma])	=DistSurv("LogLogistic(alpha;beta;[gamma])";x)
Hazard Function	LogLogisticHaz(x,alpha,beta,[gamma])	=LogLogisticHaz(alpha;beta;[gamma]) =DistHaz("LogLogistic(alpha;beta;[gamma])";x)
Cumulative Hazard Function	LogLogisticCumHaz(x,alpha,beta,[gamma])	=DistCumHaz("LogLogistic(alpha;beta;[gamma])";x)
Inverse CDF (Quantile Function)	LogLogisticInv(P,alpha,beta,[gamma])	=LogLogisticInv(alpha;beta;[gamma]) =DistInv("LogLogistic(alpha;beta;[gamma])";P)
Random Numbers	LogLogisticRand(alpha,beta,[gamma])	=LogLogisticRand(alpha;beta;[gamma]) =DistRand("LogLogistic(alpha;beta;[gamma])")
Mode	LogLogisticMode(alpha,beta,[gamma])	=DistMode("LogLogistic(alpha;beta;[gamma])")
Mean	LogLogisticMean(alpha,beta,[gamma])	=LogLogisticMean(alpha;beta;[gamma]) =DistMean("LogLogistic(alpha;beta;[gamma])")
Variance	LogLogisticVar(alpha,beta,[gamma])	=LogLogisticVar(alpha;beta;[gamma]) =DistVar("LogLogistic(alpha;beta;[gamma])")
Standard Deviation	LogLogisticStdev(alpha,beta,[gamma])	=LogLogisticStdev(alpha;beta;[gamma]) =DistStdev("LogLogistic(alpha;beta;[gamma])")
Skewness	LogLogisticSkew(alpha,beta,[gamma])	=DistSkew("LogLogistic(alpha;beta;[gamma])")
(Excess) Kurtosis	LogLogisticKurt(alpha,beta,[gamma])	=DistKurt("LogLogistic(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).