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
• 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

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

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