Understand the distribution
What the kumaraswamy distribution calculator models
Modeling values inside known endpoints. Bounded distributions assign no probability outside their declared support. Shape parameters or a mode determine how density is arranged between the endpoints.
1Declare the finite support2Set shape, mode, or endpoint parameters3Evaluate positions and intervals inside the bounds
Density and cumulative rule
F(x)=1−(1−x^a)^b and f(x)=abx^(a−1)(1−x^a)^(b−1), 0≤x≤1.
A density height is not itself a probability. Continuous probability is the area accumulated across an interval.
Interpretation and limits
The model offers beta-like bounded shapes with closed-form cumulative probability and quantiles, but it is a distinct family.
Model boundary: Both shape parameters must be positive and observations must lie in the closed unit interval; endpoints may have unbounded density.
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 kumaraswamy distribution calculator works
F(x)=1−(1−x^a)^b and f(x)=abx^(a−1)(1−x^a)^(b−1), 0≤x≤1.
The model offers beta-like bounded shapes with closed-form cumulative probability and quantiles, but it is a distinct family.
Worked example
Kumaraswamy Distribution example
With a=1 and b=1, the Kumaraswamy model is uniform on zero to one.
F(x)=1−(1−x^a)^b and f(x)=abx^(a−1)(1−x^a)^(b−1), 0≤x≤1.
Supported inputs
Precision and limits
Model and design
Both shape parameters must be positive and observations must lie in the closed unit interval; endpoints may have unbounded density.
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 model offers beta-like bounded shapes with closed-form cumulative probability and quantiles, but it is a distinct family.
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.
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