alvarezcl - 4 months ago 35

Python Question

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?

Answer

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