atoti.stats.beta.pdf()#

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

Probability density function for a beta distribution.

Warning

This feature is experimental, its key is "stats.beta.pdf".

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:

MeasureDefinition