Gamma Distribution Calculator
Evaluate a shape–scale gamma CDF and density with the scale convention stated explicitly.
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Result
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Calculation steps
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How to calculate
Use the shape/scale parameterization and regularized upper incomplete gamma to evaluate the lower cumulative probability.
CDF=1−Q(k,x/θ); density=exp((k−1)ln x−x/θ−ln Γ(k)−k ln θ)
Worked example
Shape 2 and scale 3 at x=6 give CDF 1−3exp(−2)≈0.59399415, mean 6 and variance 18.
Assumptions and input details
Shape 0.5–1000 and positive query/scale. Scale is the reciprocal of a rate parameter. No parameter fitting; endpoint singular densities at x=0 are outside the input scope.
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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