Python模拟实现高斯分布拟合

import numpy as np
import scipy as sp
from scipy import stats
import matplotlib.pyplot as plt

## generate the data and plot it for an ideal normal curve

## x-axis for the plot
x_data = np.arange(-5, 5, 0.001)

## y-axis as the gaussian
y_data = stats.norm.pdf(x_data, 0, 1)

## plot data
plt.plot(x_data, y_data)

#Define the Gaussian function
def gauss(x, H, A, x0, sigma):
	return H + A * np.exp(-(x - x0) ** 2 / (2 * sigma ** 2))

import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
xdata = [ -10.0, -9.0, -8.0, -7.0, -6.0, -5.0, -4.0, -3.0, -2.0, -1.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0]
ydata = [1.2, 4.2, 6.7, 8.3, 10.6, 11.7, 13.5, 14.5, 15.7, 16.1, 16.6, 16.0, 15.4, 14.4, 14.2, 12.7, 10.3, 8.6, 6.1, 3.9, 2.1]

# Recast xdata and ydata into numpy arrays so we can use their handy features
xdata = np.asarray(xdata)
ydata = np.asarray(ydata)
plt.plot(xdata, ydata, 'o')

# Define the Gaussian function
def Gauss(x, A, B):
	y = A*np.exp(-1*B*x**2)
	return y
parameters, covariance = curve_fit(Gauss, xdata, ydata)

fit_A = parameters[0]
fit_B = parameters[1]

fit_y = Gauss(xdata, fit_A, fit_B)
plt.plot(xdata, ydata, 'o', label='data')
plt.plot(xdata, fit_y, '-', label='fit')
plt.legend()

import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as mpl

# Let's create a function to model and create data
def func(x, a, x0, sigma):
	return a*np.exp(-(x-x0)**2/(2*sigma**2))

# Generating clean data
x = np.linspace(0, 10, 100)
y = func(x, 1, 5, 2)

# Adding noise to the data
yn = y + 0.2 * np.random.normal(size=len(x))

# Plot out the current state of the data and model
fig = mpl.figure()
ax = fig.add_subplot(111)
ax.plot(x, y, c='k', label='Function')
ax.scatter(x, yn)

# Executing curve_fit on noisy data
popt, pcov = curve_fit(func, x, yn)

#popt returns the best fit values for parameters of the given model (func)
print (popt)

ym = func(x, popt[0], popt[1], popt[2])
ax.plot(x, ym, c='r', label='Best fit')
ax.legend()
fig.savefig('model_fit.png')