Matplotlib

Exercise 11.1: Plotting a function

Plot the function    f(x) = sin2(x − 2)e−x2    over the interval [0, 2]. Add proper axis labels, a title, etc.

import matplotlib

print(matplotlib.get_backend())
import matplotlib.pyplot as plt
import numpy as np


x1 = np.linspace(0, 2, 1000) 
def y1(x1):
	x2 = x1 - 2
	x3 = x1**2
	y1 = (np.sin(x2)**2)*np.exp(-x3)
	return y1

plt.plot(x1, y1(x1), 'r-',linewidth=1,label='f(x)')
plt.title('y = $sin^2(x-2){e^{-x^2}}$')
plt.show()

result:

Exercise 11.2: Data

Create a data matrix X with 20 observations of 10 variables. Generate a vector b with parameters Then generate the response vector y = Xb+z where z is a vector with standard normally distributed variables.Now (by only using y and X), find an estimator for b, by solving

ˆb = arg min ∥Xb − y∥2b

Plot the true parameters b and estimated parameters ˆb. See Figure 1 for an example plot.

import matplotlib

print(matplotlib.get_backend())
import matplotlib.pyplot as plt
import numpy as np
from scipy import linalg

X = np.random.randint(1,10,size=(20,10))  
z = np.random.normal(0,1,size=(20,1))
b = np.random.rand(10,1)

y = np.dot(X,b) + z
x = np.linspace(0.0, 1.0, 10) 

_b = np.array(linalg.lstsq(X, y))[0]


plt.scatter(x,b,c='r',marker='o',label='b')
plt.scatter(x,_b,c='b',marker='o',label='b^')

plt.legend()
plt.title('Parameter plot')
plt.show()

result:

Exercise 11.3: Histogram and density estimation

Generate a vector z of 10000 observations from your favorite exotic distribution. Then make a plot thatshows a histogram of z (with 25 bins), along with an estimate for the density, using a Gaussian kerneldensity estimator (see scipy.stats). See Figure 2 for an example plot.

import matplotlib

print(matplotlib.get_backend())
import matplotlib.pyplot as plt
import numpy as np
from scipy import linalg
from scipy import stats


z = np.random.normal(1,100,size=10000)
x = np.linspace(-400,400,1000)

plt.hist(z, 25,density=True)

kernel = stats.gaussian_kde(z)

plt.plot(x,kernel.evaluate(x))
plt.title('Parameter plot')
plt.show()

result: