atoti.experimental.stats.normal module#

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

For more information read:

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

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

  • mean (NumericMeasureConvertible) – The mean value of the distribution.

  • standard_deviation (NumericMeasureConvertible) – The standard deviation of the distribution. Must be positive.

Return type

MeasureDescription

See also

cdf of a normal distribution on Wikipedia

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

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

  • mean (NumericMeasureConvertible) – The mean value of the distribution.

  • standard_deviation (NumericMeasureConvertible) – The standard deviation of the distribution. Must be positive.

Return type

MeasureDescription

See also

General normal distribution on Wikipedia.

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

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

  • mean (NumericMeasureConvertible) – The mean value of the distribution.

  • standard_deviation (NumericMeasureConvertible) – The standard deviation of the distribution. Must be positive.

Return type

MeasureDescription

See also

Quantile function of a normal distribution on Wikipedia