# atoti.experimental.stats.chi2 module#

Chi-square distribution.

atoti.experimental.stats.chi2.cdf(point, /, *, degrees_of_freedom)#

Cumulative distribution function for a chi-square distribution.

The cdf of the chi-square distribution with k degrees of freedom is

$\operatorname {cdf}(x)=\dfrac {\gamma (\frac {k}{2},\,\frac {x}{2})}{\Gamma (\frac {k}{2})}$

where $$\Gamma$$ is the gamma function and $$\gamma$$ the lower incomplete gamma function.

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

• degrees_of_freedom (NumericMeasureConvertible) – The number of degrees of freedom. Must be positive.

Return type

MeasureDescription

atoti.experimental.stats.chi2.pdf(point, /, *, degrees_of_freedom)#

Probability density function for a chi-square distribution.

The pdf of the chi-square distribution with k degrees of freedom is

$\operatorname {pdf}(x)=\dfrac {x^{\frac {k}{2}-1}e^{-\frac {x}{2}}} {2^\frac {k}{2}\Gamma \left(\frac {k}{2}\right)}$

where $$\Gamma$$ is the gamma function.

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

• degrees_of_freedom (NumericMeasureConvertible) – The number of degrees of freedom. Must be positive.

Return type

MeasureDescription

atoti.experimental.stats.chi2.ppf(point, /, *, degrees_of_freedom)#

Percent point function for a chi-square distribution.

Also called inverse cumulative distribution function.

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

• degrees_of_freedom (NumericMeasureConvertible) – The number of degrees of freedom. Must be positive.

Return type

MeasureDescription