Curve Fiting Of Normal Distribution In Python

I want to calculate the percentiles of normal distribution data, so I first fit the data to the normal distribution, here is the example: from scipy.stats import norm import numpy

Solution 1:

depends on what you plotted, these look OK to me:

plt.plot(x,y)
Out[3]: [<matplotlib.lines.Line2D at 0xb9cef98>]

popt,popc
Out[4]: 
(array([  8.41765250e+04,   1.98651581e+00,   3.15537860e+00]),
 array([[  5.64670700e+05,   1.12782889e-05,   1.15455042e+01],
        [  1.12782889e-05,   2.91058556e-06,   2.73909077e-10],
        [  1.15455042e+01,   2.73909077e-10,   2.88523818e-04]]))

plt.plot(x,datafit(x,*popt))
Out[5]: [<matplotlib.lines.Line2D at 0xb990080>]

my guess is that you've got an error in sig, scale and *,/ in your datafit def vs norm()

I rewrote datafit to match the scipy norm.pdf

and still have a factor of ~pi issue which may be just definitional: https://en.wikipedia.org/wiki/Normal_distribution

oops, looks like the "factor of pi" was just coincidence of your particular data rereading the norm.pdf def suggest the whole is rescaled by the 'scale" factor so now I think it should be:

'''
norm.pdf(x) = exp(-x**2/2)/sqrt(2*pi)
norm.pdf(x, loc, scale) == norm.pdf(y) / scale with y = (x - loc) / scale
'''defdatafit(x,N,u,sig):
#    y = N/(np.sqrt(2*np.pi)*sig)*np.exp(-(x-u)**2/2*sig**2)
    y = N*np.exp(-((x-u)/sig)**2/2)/(np.sqrt(2*np.pi))
    return y
popt,popc = curve_fit(datafit,x,y,p0=[np.max(y),2,2])

# scipy norm.pdf with scaling factors to match datafit()
Normal_distribution = popt[0]*popt[2]*norm.pdf(x, popt[1], popt[2])

plt.plot(x,y, 'b')
plt.plot(x, datafit(x+.1, *popt), 'g')
plt.plot(x, Normal_distribution, 'r')