PYTHON

sns.distplot fit

from scipy import stats

ax = sns.distplot(e_t_hat, bins=20, kde=False, fit=stats.norm);
plt.title('Distribution of Cointegrating Spread for Brent and Gasoil')

# Get the fitted parameters used by sns
(mu, sigma) = stats.norm.fit(e_t_hat)
print "mu={0}, sigma={1}".format(mu, sigma)

# Legend and labels 
plt.legend(["normal dist. fit ($mu=${0:.2g}, $sigma=${1:.2f})".format(mu, sigma)])
plt.ylabel('Frequency')

# Cross-check this is indeed the case - should be overlaid over black curve
x_dummy = np.linspace(stats.norm.ppf(0.01), stats.norm.ppf(0.99), 100)
ax.plot(x_dummy, stats.norm.pdf(x_dummy, mu, sigma))
plt.legend(["normal dist. fit ($mu=${0:.2g}, $sigma=${1:.2f})".format(mu, sigma),
           "cross-check"])