import matplotlib.pyplot as plt
import numpy as np
import scipy.stats as st
import arviz as az
plt.style.use('arviz-darkgrid')
x = np.linspace(0, 5, 200)
for b in [0.5, 1.0, 2.0]:
    pdf = st.cauchy.pdf(x, scale=b)
    plt.plot(x, pdf, label=r'$\beta$ = {}'.format(b))
plt.xlabel('x', fontsize=12)
plt.ylabel('f(x)', fontsize=12)
plt.legend(loc=1)
plt.show()