atoti.experimental.stats package¶
Submodules¶
atoti.experimental.stats.beta module¶
Beta distribution.
For more information read:
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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
See also
- Return type
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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
See also
- Return type
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atoti.experimental.stats.beta.ppf(point, *, alpha, beta)¶ Percent point function for a beta distribution.
Also called inverse cumulative distribution function.
- Parameters
See also
- Return type
atoti.experimental.stats.chi2 module¶
Chi-square distribution.
For more information read:
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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
See also
- Return type
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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
See also
- Return type
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atoti.experimental.stats.chi2.ppf(point, *, degrees_of_freedom)¶ Percent point function for a chi-square distribution.
Also called inverse cumulative distribution function.
- Parameters
See also
- Return type
atoti.experimental.stats.f module¶
F-distribution, also known as Snedecor’s F distribution or the Fisher–Snedecor distribution.
For more information read:
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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 (
Measure) – The point where the function is evaluated.numerator_degrees_of_freedom (
Union[int,float,Measure,MeasureConvertible]) – Numerator degrees of freedom. Must be positive.denominator_degrees_of_freedom (
Union[int,float,Measure,MeasureConvertible]) – Denominator degrees of freedom. Must be positive.
See also
- Return type
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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 (
Measure) – The point where the function is evaluated.numerator_degrees_of_freedom (
Union[int,float,Measure,MeasureConvertible]) – Numerator degrees of freedom. Must be positive.denominator_degrees_of_freedom (
Union[int,float,Measure,MeasureConvertible]) – Denominator degrees of freedom. Must be positive.
See also
- Return type
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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 (
Measure) – The point where the function is evaluated.numerator_degrees_of_freedom (
Union[int,float,Measure,MeasureConvertible]) – Numerator degrees of freedom. Must be positive.denominator_degrees_of_freedom (
Union[int,float,Measure,MeasureConvertible]) – Denominator degrees of freedom. Must be positive.
See also
- Return type
atoti.experimental.stats.normal module¶
Normal distribution, also called Gaussian, Gauss or Laplace–Gauss distribution.
For more information read:
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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
See also
cdf of a normal distribution on Wikipedia
- Return type
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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
See also
General normal distribution on Wikipedia.
- Return type
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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
See also
Quantile function of a normal distribution on Wikipedia
- Return type
atoti.experimental.stats.t module¶
Student’s t distribution.
For more information read:
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atoti.experimental.stats.t.cdf(point, *, degrees_of_freedom)¶ Cumulative distribution function for a Student’s t distribution.
- Parameters
See also
- Return type
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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
See also
- Return type
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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
See also
- Return type
Module contents¶
Warning
Experimental features are subject to breaking changes (even removals) in minor and/or patch releases.