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 \(d1\) 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
See also
- 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
See also
- 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