atoti.experimental.stats.f module#

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

For more information read:

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 $d 1$ et $d 2$ is

cdf (x) = I_{\frac{d_{1} x}{d_{1} x + d_{2}}} (\frac{d_{1}}{2}, \frac{d_{2}}{2})

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

See also

The F-distribution Wikipedia page

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 $d 1$ et $d 2$ is

pdf (x) = \frac{\sqrt{\frac{(d_{1} x)^{d_{1}} d_{2}^{d_{2}}}{(d_{1} x + d_{2})^{d_{1} + d_{2}}}}}{x B (\frac{d_{1}}{2}, \frac{d_{2}}{2})}

Where $B$ 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

See also

The F-distribution Wikipedia page

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

See also

The F-distribution Wikipedia page