alvarezcl - 3 months ago 19
Python Question

# How can I find the right gaussian curve given some data?

I have code that draws from a gaussian in 1D:

``````import numpy as np
from scipy.stats import norm
from scipy.optimize import curve_fit
import matplotlib.mlab as mlab
import matplotlib.pyplot as plt
import gauss

# Beginning in one dimension:
mean = 0; Var = 1; N = 1000
scatter = np.random.normal(mean,np.sqrt(Var),N)
scatter = np.sort(scatter)
mu,sigma = norm.fit(scatter)
``````

I obtain mu and sigma using norm.fit()

Now I'd like to obtain my parameters using

``````xdata = np.linspace(-5,5,N)
pop, pcov = curve_fit(gauss.gauss_1d,xdata,scatter)
``````

The problem is I don't know how to map my scattered points (drawn from a 1D gaussian) to the x-line in order to use curve_fit.

Also, suppose I simply use and mu and sigma as earlier.

I plot using:

``````n, bins, patches = plt.hist(scatter,50,facecolor='green')
y = 2*max(n)*mlab.normpdf(bins,mu,sigma)
l = plt.plot(bins,y,'r--')

plt.xlabel('x-coord')
plt.ylabel('Occurrences')
plt.grid(True)
plt.show()
``````

But I have to guess the amplitude as 2*max(n). It works but it's not robust. How can I find the amplitude without guessing?

To avoid guessing the amplitude, call `hist()` with `normed=True`, then the amplitude corresponds to `normpdf()`.

For doing a curve fit, I suggest to use not the density but the cumulative distribution: Each sample has a height of `1/N`, which successively sum up to 1. This has the advantage that you don't need to group samples in bins.

``````import numpy as np
from scipy.stats import norm
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt

# Beginning in one dimension:
mean = 0; Var = 1; N = 100
scatter = np.random.normal(mean,np.sqrt(Var),N)
scatter = np.sort(scatter)
mu1,sigma1 = norm.fit(scatter) # classical fit

scat_sum = np.cumsum(np.ones(scatter.shape))/N # cumulative samples
[mu2,sigma2],Cx = curve_fit(norm.cdf, scatter, scat_sum, p0=[0,1]) # curve fit
print(u"norm.fit():  µ1= {:+.4f}, σ1={:.4f}".format(mu1, sigma1))
print(u"curve_fit(): µ2= {:+.4f}, σ2={:.4f}".format(mu2, sigma2))

fg = plt.figure(1); fg.clf()
ax = fg.add_subplot(1, 1, 1)
t = np.linspace(-4,4, 1000)
ax.plot(t, norm.cdf(t, mu1, sigma1), alpha=.5, label="norm.fit()")
ax.plot(t, norm.cdf(t, mu2, sigma2), alpha=.5, label="curve_fit()")
ax.step(scatter, scat_sum, 'x-', where='post', alpha=.5, label="Samples")
ax.legend(loc="best")
ax.grid(True)
ax.set_xlabel("\$x\$")
ax.set_ylabel("Cumulative Probability Density")
ax.set_title("Fit to Normal Distribution")

fg.canvas.draw()
plt.show()
``````

prints

``````norm.fit():  µ1= +0.1534, σ1=1.0203
curve_fit(): µ2= +0.1135, σ2=1.0444
``````

and plots