Random number generation from an arbitrary probability density function

Question

I would like to be able to generate random numbers with a probability density function that comes from a drawn curve. The two below have the same area under the curve, but should create lists of random numbers with different characteristics.

My intuition is that one way would be to sample the curve, and then use the areas of these rectangles to feed np.random.choice, to select a range, to make a normal random case in the range of this range of rectangles.

This is not a very effective way to do this. Is there a more “right” way to do this?

I actually had a crack:

import matplotlib.pyplot as plt
import numpy as np

areas = [4.397498, 4.417111, 4.538467, 4.735034, 4.990129, 5.292455, 5.633938,
         6.008574, 6.41175, 5.888393, 2.861898, 2.347887, 2.459234, 2.494357,
         2.502986, 2.511614, 2.520243, 2.528872, 2.537501, 2.546129, 7.223747,
         7.223747, 2.448148, 1.978746, 1.750221, 1.659351, 1.669999]
divisons = [0.0, 0.037037, 0.074074, 0.111111, 0.148148, 0.185185, 0.222222,
            0.259259, 0.296296, 0.333333, 0.37037, 0.407407, 0.444444, 0.481481,
            0.518519, 0.555556, 0.592593, 0.62963, 0.666667, 0.703704, 0.740741,
            0.777778, 0.814815, 0.851852, 0.888889, 0.925926, 0.962963, 1.0]
weights = [a/sum(areas) for a in areas]
indexes = np.random.choice(range(len(areas)), 50000, p=weights)
samples = []
for i in indexes:
    samples.append(np.random.uniform(divisons[i], divisons[i+1]))

binwidth = 0.02
binSize = np.arange(min(samples), max(samples) + binwidth, binwidth)
plt.hist(samples, bins=binSize)
plt.xlim(xmax=1)
plt.show()

The method works, but a little harder!

Answer 1

, , , , .

, y ( y- ) _ , .

from numpy.random import choice
pde = choice(list_of_candidates, number_of_items_to_pick, p=probability_distribution)

_ ( y y ) - , list_of_candidates ( x). replace = False, , .

. numpy docs

, pde, , pde.

EDIT: . pde, numba (http://numba.pydata.org) for.

Answer 2

- rv_continuous scipy.stats. pdf rv_continuous. , , pdf, cdf .

Answer 3

Another method is to reverse the CDF. Then you use a single random generator to generate p values ​​on the x axis of the inverse CDF to generate random accesses of your PDF. See This Article: http://matlabtricks.com/post-44/generate-random-numbers-with-a-given-distribution