Beta distribution Probabilities
Calculator of Beta distribution : probabilities, density function (PDF) and cumulative density function (CDF).
Beta Distribution formulas
Notations
X : a random variable following a beta distribution
`alpha` : shape parameter (> 0)
`beta` : second shape parameter (> 0)
Probability Density Function (PDF)
For x between 0 and 1 (inclusive),
`f(x) = (Gamma(alpha+beta))/(Gamma(alpha)*Gamma(beta))*x^(alpha-1)(1-x)^(beta-1)`
`Gamma(x)` is the gamma function.
Cumulative distribution function (CDF)
`F(x) = \int_-oo^x f(t)\ dt`
`F(x) = (Gamma(alpha+beta))/(Gamma(alpha)*Gamma(beta))*\int_-oo^xt^(alpha-1)(1-t)^(beta-1)\ dt`
Probabilities
Probability that X is greater than a :
`P(X > a) = 1 - F(a)`
Probability that X is less than b :
`P(X < b) = F(b)`
Probability that X lies between a and b :
`P(a < X < b) = F(b) - F(a)`
See also
Inverse Beta distribution Calculator
Beta distribution Chart
Statistics Calculators