Outcome

loglogistic(γ, β, α, stream) is a non-negative continuous probability distribution. 

γ is the location parameter ∈ ( - ∞, ∞ ) 
β is the scale parameter ( 0, ∞ ) 
α is the shape parameter ( 0, ∞ ) 
stream is a reference to one of the random number streams {0,1,2,...} 

range = ( γ, ∞ ) 
mean = γ + β(π⁄α)csc(π⁄α) for α > 1 
variance = β²(π⁄α){2csc(2π⁄α) − (π⁄α)[csc(π⁄α)]²} for α > 2 

Used to model the time to perform some task.

loglogistic(0, 1, 2, 5); 

A loglogistic distribution with a location (shift) of 0, a scale of 1, a shape factor of 2 and random stream number 5.