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 (
MeasureDescription) – The point where the function is evaluated.mean (
Union[int,float,MeasureDescription,MeasureConvertible]) – The mean value of the distribution.standard_deviation (
Union[int,float,MeasureDescription,MeasureConvertible]) – The standard deviation of the distribution. Must be positive.
See also
cdf of a normal distribution on Wikipedia
- Return type
- 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 (
MeasureDescription) – The point where the function is evaluated.mean (
Union[int,float,MeasureDescription,MeasureConvertible]) – The mean value of the distribution.standard_deviation (
Union[int,float,MeasureDescription,MeasureConvertible]) – The standard deviation of the distribution. Must be positive.
See also
General normal distribution on Wikipedia.
- Return type
- 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 (
MeasureDescription) – The point where the function is evaluated.mean (
Union[int,float,MeasureDescription,MeasureConvertible]) – The mean value of the distribution.standard_deviation (
Union[int,float,MeasureDescription,MeasureConvertible]) – The standard deviation of the distribution. Must be positive.
See also
Quantile function of a normal distribution on Wikipedia
- Return type