Calculating the derivative of cumulative density function in Python
The derivative of the CDF is the PDF.
Here is an approximation of the derivative of the CDF:
dx = x[1]-x[0]deriv = np.diff(wei.cdf(x))/dximport scipy.stats as simport matplotlib.pyplot as pltimport numpy as npwei = s.weibull_min(2, 0, 2) # shape, loc, scale - creates weibull objectsample = wei.rvs(1000)shape, loc, scale = s.weibull_min.fit(sample, floc=0) x = np.linspace(np.min(sample), np.max(sample))dx = x[1]-x[0]deriv = np.diff(wei.cdf(x))/dxplt.hist(sample, normed=True, fc="none", ec="grey", label="frequency")plt.plot(x, wei.cdf(x), label="cdf")plt.plot(x, wei.pdf(x), label="pdf")plt.plot(x[1:]-dx/2, deriv, label="derivative")plt.legend(loc=1)plt.show()yields
Note that the x-locations associated with deriv have been shifted by dx/2 so the approximation is centered between the values used to compute it.