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Beta Distribution Density Calculator — result sheet
Evaluate the beta probability density and mean for a selected shape pair and value.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: f(x)=x^(α−1)(1−x)^(β−1)/B(α,β); mean=α/(α+β).
The selected point density and distribution mean are shown separately; a density is not itself a probability for one exact point.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Alpha shape — minimum 0.001; maximum 1000
- Beta shape — minimum 0.001; maximum 1000
- Value x — minimum 1.0E-6; maximum 0.999999
Worked example
| Input | Value |
|---|---|
| Alpha shape | 2 |
| Beta shape | 5 |
| Value x | 0.3 |
Density ≈2.1609; mean ≈0.2857.
Assumptions and limits
- Alpha and beta are positive shape parameters and x is strictly between zero and one.
- The beta density is evaluated with a numerically stable log-gamma implementation.
- Interval probabilities, posterior modeling, and parameter estimation are not inferred.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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