atoti.experimental.stats.beta.pdf()#

atoti.experimental.stats.beta.pdf(point, /, *, alpha, beta)#

Probability density function for a beta distribution.

The pdf of the beta distribution with shape parameters \(\alpha\) and \(\beta\) is given by the formula

\[\operatorname {pdf}(x) = \frac {x^{\alpha -1}(1-x)^{\beta -1}}{ \mathrm {B}(\alpha ,\beta )}\]

With \(\mathrm {B}\) the beta function:

\[\mathrm {B} (\alpha ,\beta )=\int _{0}^{1}t^{\alpha -1}(1-t)^{\beta-1}dt = \frac {\Gamma (\alpha )\Gamma (\beta )}{\Gamma (\alpha +\beta )}\]

Where \(\Gamma\) is the Gamma function.

Parameters:

point (VariableMeasureConvertible) – The point where the function is evaluated.
alpha (NumericMeasureConvertible) – The alpha parameter of the distribution.
beta (NumericMeasureConvertible) – The beta parameter of the distribution.

Return type:

MeasureDescription