# atoti.experimental.stats package¶

## atoti.experimental.stats.beta module¶

Beta distribution.

atoti.experimental.stats.beta.cdf(point, *, alpha, beta)

Cumulative distribution function for a beta distribution.

The cdf of the beta distribution with shape parameters $$\alpha$$ and $$\beta$$ is

$\operatorname {cdf}(x) = I_x(\alpha,\beta)$

Where $$I$$ is the regularized incomplete beta function.

Parameters
Return type

Measure

atoti.experimental.stats.beta.pdf(point, *, alpha, beta)

Probability density function for a beta distribution.

The pdf of the beta distribution with shape parameters $$\alpha$$ and $$\beta$$ is given by the formula

$\operatorname {pdf}(x) = \frac {x^{\alpha -1}(1-x)^{\beta -1}}{ \mathrm {B}(\alpha ,\beta )}$

With $$\mathrm {B}$$ the beta function:

$\mathrm {B} (\alpha ,\beta )=\int _{0}^{1}t^{\alpha -1}(1-t)^{\beta-1}dt = \frac {\Gamma (\alpha )\Gamma (\beta )}{\Gamma (\alpha +\beta )}$

Where $$\Gamma$$ is the Gamma function.

Parameters
Return type

Measure

atoti.experimental.stats.beta.ppf(point, *, alpha, beta)

Percent point function for a beta distribution.

Also called inverse cumulative distribution function.

Parameters
Return type

Measure

## 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
Return type

Measure

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
Return type

Measure

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

Percent point function for a chi-square distribution.

Also called inverse cumulative distribution function.

Parameters
Return type

Measure

## 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
Return type

Measure

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
Return type

Measure

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
Return type

Measure

## atoti.experimental.stats.normal module¶

Normal distribution, also called Gaussian, Gauss or Laplace–Gauss distribution.

atoti.experimental.stats.normal.cdf(point, *, mean, standard_deviation)

Cumulative distribution function for a normal distribution.

The cdf is given by the formula

$\operatorname {cdf}(x) = \frac {1}{2}\left[1 + \operatorname {erf} \left(\frac {x-\mu }{\sigma {\sqrt {2}}}\right)\right]$

Where $$\mu$$ is the mean of the distribution, $$\sigma$$ is its standard deviation and $$\operatorname {erf}$$ the error function.

Parameters

cdf of a normal distribution on Wikipedia

Return type

Measure

atoti.experimental.stats.normal.pdf(point, *, mean=0, standard_deviation=1)

Probability density function for a normal distribution.

The pdf is given by the formula

$\operatorname {pdf}(x) = \frac{1}{ \sigma \sqrt{2 \pi} } e^{-\frac{1}{2} \left(\frac{x - \mu}{\sigma}\right)^{2}}$

Where $$\mu$$ is the mean (or expectation) of the distribution while $$\sigma$$ is its standard deviation.

Parameters

General normal distribution on Wikipedia.

Return type

Measure

atoti.experimental.stats.normal.ppf(point, *, mean, standard_deviation)

Percent point function for a normal distribution.

Also called inverse cumulative distribution function.

The ppf is given by the formula

$\operatorname {ppf}(x) = \mu + \sigma \sqrt{2} \operatorname {erf} ^{-1}(2x-1)$

Where $$\mu$$ is the mean of the distribution, $$\sigma$$ is its standard deviation and $$\operatorname {erf}^{-1}$$ the inverse of the error function.

Parameters
Return type

Measure

## 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
Return type

Measure

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
Return type

Measure

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
Return type

Measure

## Module contents¶

Warning

Experimental features are subject to breaking changes (even removals) in minor and/or patch releases.