Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the log-logistic distribution calculator works
F(x)=1/[1+(α/x)^β], x>0, with scale α and shape β.
The survival tail is heavier than exponential, and moments cease to exist when the shape is too small.
Worked example
Log-Logistic Distribution example
At x equal to scale α, every log-logistic model has cumulative probability 0.5.
F(x)=1/[1+(α/x)^β], x>0, with scale α and shape β.
Supported inputs
Precision and limits
Model and design
The mean exists only for shape above 1 and variance only above 2; this is not the same parameterization as a logistic model on x itself.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
The survival tail is heavier than exponential, and moments cease to exist when the shape is too small.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
Continue calculating