Beta Distribution Calculator
Calculate beta CDF, density, mean and variance for two positive shape parameters.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Evaluate the regularized incomplete beta function and the log-gamma-normalized density.
CDF=Iₓ(α,β); density=x^(α−1)(1−x)^(β−1)/B(α,β)
Worked example
Beta(2,3) at x=0.5 gives CDF 0.6875, density 1.5, mean 0.4 and variance 0.04.
Assumptions and input details
Positive shapes and interior x only avoid infinite endpoint densities. This evaluates an entered distribution without fitting observations or choosing a Bayesian prior. Density is not point probability.
References: NIST: probability distributions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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