# 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

MeasureDescription

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

MeasureDescription

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

MeasureDescription