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norm_gen.fit(self, data, **kwds)

Starting estimates for the fit are given by input arguments; for any arguments not provided with starting estimates, self._fitstart(data) is called to generate such.

One can hold some parameters fixed to specific values by passing in keyword arguments f0, f1, ..., fn (for shape parameters) and floc and fscale (for location and scale parameters, respectively).

Notes

For the normal distribution, method of moments and maximum likelihood estimation give identical fits, and explicit formulas for the estimates are available. This function uses these explicit formulas for the maximum likelihood estimation of the normal distribution parameters, so the optimizer and method arguments are ignored.

Parameters

data : array_like

Data to use in estimating the distribution parameters.

arg1, arg2, arg3,... : floats, optional

Starting value(s) for any shape-characterizing arguments (those not provided will be determined by a call to _fitstart(data)). No default value.

**kwds : floats, optional

loc: initial guess of the distribution's location parameter.
scale: initial guess of the distribution's scale parameter.

Special keyword arguments are recognized as holding certain parameters fixed:

Raises

TypeError, ValueError: If an input is invalid
`~scipy.stats.FitError`: If fitting fails or the fit produced would be invalid

Returns

parameter_tuple : tuple of floats: Estimates for any shape parameters (if applicable), followed by those for location and scale. For most random variables, shape statistics will be returned, but there are exceptions (e.g. norm).

Return estimates of shape (if applicable), location, and scale parameters from data. The default estimation method is Maximum Likelihood Estimation (MLE), but Method of Moments (MM) is also available.

Examples

Generate some data to fit: draw random variates from the `beta` distribution

from scipy.stats import beta
a, b = 1., 2.
x = beta.rvs(a, b, size=1000)

Now we can fit all four parameters (``a``, ``b``, ``loc`` and ``scale``):

a1, b1, loc1, scale1 = beta.fit(x)

We can also use some prior knowledge about the dataset: let's keep ``loc`` and ``scale`` fixed:

a1, b1, loc1, scale1 = beta.fit(x, floc=0, fscale=1)
loc1, scale1

We can also keep shape parameters fixed by using ``f``-keywords. To keep the zero-th shape parameter ``a`` equal 1, use ``f0=1`` or, equivalently, ``fa=1``:

a1, b1, loc1, scale1 = beta.fit(x, fa=1, floc=0, fscale=1)
a1

Not all distributions return estimates for the shape parameters. ``norm`` for example just returns estimates for location and scale:

from scipy.stats import norm
x = norm.rvs(a, b, size=1000, random_state=123)
loc1, scale1 = norm.fit(x)
loc1, scale1

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GitHub : /scipy/stats/_continuous_distns.py#383
type: <class 'function'>
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