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# Log-Logistic Distribution

## Parameters

- continuous shape parameter ()
- continuous scale parameter ()
- continuous location parameter ( yields the two-parameter Log-Logistic distribution)

## 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).