# atoti.experimental.stats.t module#

Student’s t distribution.

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

Cumulative distribution function for a Student’s t distribution.

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.t.pdf(point, /, *, degrees_of_freedom)#

Probability density function for a Student’s t distribution.

The pdf of a Student’s t-distribution is:

$\operatorname {pdf}(x)=\frac {\Gamma (\frac {\nu +1}{2})}{\sqrt {\nu \pi }\,\Gamma (\frac {\nu }{2})} \left(1+\frac {x^{2}}{\nu }\right)^{-\frac {\nu +1}{2}}$

where $$\nu$$ is the number of degrees of freedom and $$\Gamma$$ 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.t.ppf(point, /, *, degrees_of_freedom)#

Percent point function for a Student’s t 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