skg.gauss¶
Unnormalized Gaussian bell curve fit.
The amplitude of this function is one of the fitting parameters, unlike for the two-parameter PDF version.
The third fitting parameter, , is the amplitude of the Gaussian at . This is equivalent, up to a scaling factor, to normalizing the area under the curve, as the PDF version does.
The conversion between amplitude and normalization is given in Three-Parameter Gaussian as
For for the normalized (two parameter) Gaussian probability density
function, see gauss_pdf
. 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_fit (x, y[, sorted]) |
Gaussian bell curve fit of the form . |
model (x, a, mu, sigma) |
Compute . |
-
skg.gauss.
gauss_fit
(x, y, sorted=True)[source]¶ Gaussian bell curve fit of the form .
This implementation is based on an extentsion the approximate solution to integral equation (3), presented in Régressions et équations intégrales and extended in Extended Applications.
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: a, mu, sigma – A three-element array containing the estimated amplitude, mean and standard deviation, in that order.
Return type: References
- [Jacquelin] “Régressions et équations intégrales”, pp. 6-8.
- reei-supplement, Extended Applications, Three-Parameter Gaussian