atoti.experimental.stats.beta module#
Beta distribution.
For more information read:
- atoti.experimental.stats.beta.cdf(point, /, *, alpha, beta)#
Cumulative distribution function for a beta distribution.
The cdf of the beta distribution with shape parameters \(\alpha\) and \(\beta\) is
\[\operatorname {cdf}(x) = I_x(\alpha,\beta)\]Where \(I\) is the regularized incomplete beta function.
- Parameters
point (NonConstantMeasureConvertible) – 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
See also
- 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 (NonConstantMeasureConvertible) – 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
See also
- atoti.experimental.stats.beta.ppf(point, /, *, alpha, beta)#
Percent point function for a beta distribution.
Also called inverse cumulative distribution function.
- Parameters
point (NonConstantMeasureConvertible) – The point where the density function is evaluated.
alpha (NumericMeasureConvertible) – The alpha parameter of the distribution.
beta (NumericMeasureConvertible) – The beta parameter of the distribution.
- Return type
MeasureDescription
See also