# atoti.experimental.stats.beta module#

Beta distribution.

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

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

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