# atoti.experimental.stats.f module#

F-distribution, also known as Snedecor’s F distribution or the Fisher–Snedecor distribution.

atoti.experimental.stats.f.cdf(point, /, *, numerator_degrees_of_freedom, denominator_degrees_of_freedom)#

Cumulative distribution function for a F-distribution.

The cdf for a F-distributions with parameters $$d1$$ et $$d2$$ is

$\operatorname {cdf}(x) = I_{\frac {d_{1}x}{d_{1}x+d_{2}}} \left(\tfrac {d_{1}}{2},\tfrac {d_{2}}{2}\right)$

where I is the regularized incomplete beta function.

Parameters
• point (NonConstantMeasureConvertible) – The point where the function is evaluated.

• numerator_degrees_of_freedom (NumericMeasureConvertible) – Numerator degrees of freedom. Must be positive.

• denominator_degrees_of_freedom (NumericMeasureConvertible) – Denominator degrees of freedom. Must be positive.

Return type

MeasureDescription

atoti.experimental.stats.f.pdf(point, /, *, numerator_degrees_of_freedom, denominator_degrees_of_freedom)#

Probability density function for a F-distribution.

The pdf for a F-distributions with parameters $$d1$$ et $$d2$$ is

$\operatorname {pdf}(x) = \frac {\sqrt {\frac {(d_{1}x)^{d_{1}}\,\,d_{2}^{d_{2}}}{(d_{1}x+d_{2})^{d_{1}+d_{2}}}}} {x\,\mathrm {B} \!\left(\frac {d_{1}}{2},\frac {d_{2}}{2}\right)}$

Where $$\mathrm {B}$$ is the beta function.

Parameters
• point (NonConstantMeasureConvertible) – The point where the function is evaluated.

• numerator_degrees_of_freedom (NumericMeasureConvertible) – Numerator degrees of freedom. Must be positive.

• denominator_degrees_of_freedom (NumericMeasureConvertible) – Denominator degrees of freedom. Must be positive.

Return type

MeasureDescription

atoti.experimental.stats.f.ppf(point, /, *, numerator_degrees_of_freedom, denominator_degrees_of_freedom)#

Percent point function for a F-distribution.

Also called inverse cumulative distribution function.

Parameters
• point (NonConstantMeasureConvertible) – The point where the function is evaluated.

• numerator_degrees_of_freedom (NumericMeasureConvertible) – Numerator degrees of freedom. Must be positive.

• denominator_degrees_of_freedom (NumericMeasureConvertible) – Denominator degrees of freedom. Must be positive.

Return type

MeasureDescription