interpolated plot (pymc-devs#4557)

* interpolated plot

* interpolated minor fixes

* minor edits

* histogram fix

* relocate arviz style line position

Author: mjhajharia

pymc3/distributions/continuous.py

@@ -4223,6 +4223,28 @@ class Interpolated(BoundedContinuous):
     Both parameters ``x_points`` and values ``pdf_points`` are not variables, but
     plain array-like objects, so they are constant and cannot be sampled.
 
+    .. plot::
+
+        import matplotlib.pyplot as plt
+        import numpy as np
+        import pymc3 as pm
+        import arviz as az
+        from scipy.stats import gamma
+        plt.style.use('arviz-darkgrid')
+        rv = gamma(1.99)
+        x = np.linspace(rv.ppf(0.01),rv.ppf(0.99), 1000)
+        points = np.linspace(x[0], x[-1], 50)
+        pdf = rv.pdf(points)
+        interpolated = pm.Interpolated.dist(points, pdf)
+        fig, ax = plt.subplots(1, 1)
+        ax.plot(x, rv.pdf(x), 'C0', linestyle = '--',  label='Original Gamma pdf',alpha=0.8,lw=2)
+        ax.plot(points, pdf, color='black', marker='o', label='Lattice Points',alpha=0.5,linestyle='')
+        ax.plot(x, np.exp(interpolated.logp(x).eval()),'C1',label='Interpolated pdf',alpha=0.8,lw=3)
+        r = interpolated.random(size=1000)
+        ax.hist(r, density=True, alpha=0.4,align ='mid',color='grey')
+        ax.legend(loc='best', frameon=False)
+        plt.show()
+
     ========  ===========================================
     Support   :math:`x \in [x\_points[0], x\_points[-1]]`
     ========  ===========================================