Beta Distribution Calculator

Your details

First shape parameter. Must be positive. Values above 1 pull the distribution away from 0; values below 1 create a J-shape toward 0.
Second shape parameter. Must be positive. Values above 1 pull the distribution away from 1; values below 1 create a J-shape toward 1.
Choose the type of probability to compute. Cumulative is the standard CDF; upper tail is 1 minus the CDF; range computes the probability between two bounds.
The point at which to evaluate the PDF and CDF. Must be between 0 and 1.
ProbabilityUnimodal, right-skewed (peak near 0)
0.579825

The selected probability (CDF, tail, or range)

PDF f(x)2.1609
Mean0.285714
Variance0.0255102
Standard deviation0.159719
Mode0.2000
Median (approx.)0.263158
Skewness0.596285
ShapeUnimodal, right-skewed (peak near 0)
0.57982565.5% below · x (0 to 1)

Beta(2, 5) - Unimodal, right-skewed (peak near 0)

  • The mean is 0.2857, so the distribution is centred around 28.6% of the [0, 1] range.
  • The standard deviation is 0.1597, giving a coefficient of variation of 55.9%.
  • The distribution is right-skewed (skewness = 0.596).
  • The computed probability for x at or below 0.3 is 57.983%.

Next stepBeta is greater than alpha, so values near 0 are more probable. This is consistent with a prior that expects success rates below 50%.

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