atoti.experimental.stats.normal module

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

For more information read:

• scipy.stats.norm

• The Normal distribution Wikipedia page

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

Cumulative distribution function for a normal distribution.

The cdf is given by the formula

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

Where $\mu$ is the mean of the distribution, $\sigma$ is its standard deviation and $\mathrm{erf}$ 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

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

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

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

Where $\mu$ is the mean of the distribution, $\sigma$ is its standard deviation and ${\mathrm{erf}}^{-1}$ 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