skg.gauss_pdf

Gaussian probability density fit.

The function in this module is normalized to one, as a PDF should be:

f(x) = \frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{1}{2} \left(\frac{x - \mu}{\sigma}\right)^2} \quad \int_{-\infty}^{+\infty} f(t)dt = 1

For for the unnormalized Gaussian (with an additional amplitude parameter), see gauss. For the CDF, see gauss_cdf.

Todo

Add proper handling of colinear inputs (and other singular matrix cases).

Todo

Add tests.

Todo

Add nan_policy argument.

Todo

Add axis parameter. Figure out how to do it properly.

Todo

Add PEP8 check to formal tests.

Todo

Include amplitude in integrals.

Todo

Allow broadcasting of x and y, not necessarily identical size

Functions

gauss_pdf_fit(x, y[, sorted]) Gaussian PDF fit of the form \frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{1}{2}\left(\frac{x - \mu}{\sigma}\right)^2}.
model(x, mu, sigma) Compute y = \frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{1}{2}\left(\frac{x - \mu}{\sigma}\right)^2}.
skg.gauss_pdf.gauss_pdf_fit(x, y, sorted=True)[source]

Gaussian PDF fit of the form \frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{1}{2}\left(\frac{x - \mu}{\sigma}\right)^2}.

This implementation is based on the approximate solution to integral equation (3), presented in Régressions et équations intégrales.

Parameters:
  • x (array-like) – The x-values of the data points. The fit will be performed on a raveled version of this array.
  • y (array-like) – The y-values of the data points corresponding to x. Must be the same size as x. The fit will be performed on a raveled version of this array.
  • sorted (bool) – Set to True if x is already monotonically increasing or decreasing. If False, x will be sorted into increasing order, and y will be sorted along with it.
Returns:

mu, sigma – A two-element array containing the estimated mean and standard deviation, in that order.
Return type:

ndarray

References

skg.gauss_pdf.model(x, mu, sigma)[source]

Compute y = \frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{1}{2}\left(\frac{x - \mu}{\sigma}\right)^2}.

Parameters:
  • x (array-like) – The value of the model will be the same shape as the input.
  • mu (float) – The mean.
  • sigma (float) – The standard deviation.
Returns:

y – An array of the same shape as x, containing the model computed for the given parameters.
Return type:

array-like