CODEWITHSUNDEEP
pythonmatplotlibscipy
StarStrides
StarStrides

Reputation: 121

norm fit producing incorrect fit

Why does the following produce an incorrect output for muf and stdf?

import numpy as np
from scipy.stats import norm
x=np.linspace(-50,50,100)
sig=10
mu=0
y=1/np.sqrt(2*sig*sig*np.pi)*np.exp(-(x-mu)*(x-mu)/(2*sig*sig))
muf, stdf = norm.fit(y)
print muf,stdf

This prints 0.00989999568634 0.0134634293279

Thanks.

Upvotes: 2

Views: 1915

Answers (2)

MB-F
MB-F

Reputation: 23647

You misunderstood the purpose of norm.fit. It does not fit a Gaussian to a curve but fits a normal distribution to data:

np.random.seed(42)

y = np.random.randn(10000) * sig + mu
muf, stdf = norm.fit(y)
print(muf, stdf)
# -0.0213598336843 10.0341220613

You can use curve_fit to match the Normal distribution's parameters to a given curve, as it has been attempted originally in the question:

import numpy as np
from scipy.stats import norm
from scipy.optimize import curve_fit

x=np.linspace(-50,50,100)
sig=10
mu=0
y=1/np.sqrt(2*sig*sig*np.pi)*np.exp(-(x-mu)*(x-mu)/(2*sig*sig))

(muf, stdf), covf = curve_fit(norm.pdf, x, y, p0=[0, 1])
print(muf, stdf)
# 2.4842347485e-08 10.0000000004

Upvotes: 3

ImportanceOfBeingErnest
ImportanceOfBeingErnest

Reputation: 339695

The documentation of scipy.stats.norm says for its fit function

fit(data, loc=0, scale=1) Parameter estimates for generic data.

To me this is highly ununderstandable and I'm pretty sure that one cannot expect this function to return a fit in the usual sense.

However, to fit a gaussian is rather straight forward:

from __future__ import division
import numpy as np

x=np.linspace(-50,50,100)
sig=10
mu=0
y=1/np.sqrt(2*sig*sig*np.pi)*np.exp(-(x-mu)*(x-mu)/(2*sig*sig))  #

def gaussian_fit(xdata,ydata):
    mu = np.sum(xdata*ydata)/np.sum(ydata)
    sigma = np.sqrt(np.abs(np.sum((xdata-mu)**2*ydata)/np.sum(ydata)))
    return mu, sigma

print gaussian_fit(x,y)

This prints (-7.474196315587989e-16, 9.9999422983567516) which is sufficiently close to the expected values of (0, 10).

Upvotes: 3

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