def test_zipfian_asymptotic(self):
# test limiting case that zipfian(a, n) -> zipf(a) as n-> oo
a = 6.5
N = 10000000
k = np.arange(1, 21)
assert_allclose(zipfian.pmf(k, a, N), zipf.pmf(k, a))
assert_allclose(zipfian.cdf(k, a, N), zipf.cdf(k, a))
assert_allclose(zipfian.sf(k, a, N), zipf.sf(k, a))
assert_allclose(zipfian.stats(a, N, moments='msvk'),
zipf.stats(a, moments='msvk'))
from scipy.stats import zipf
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)
# Calculate a few first moments:
a = 6.5
mean, var, skew, kurt = zipf.stats(a, moments='mvsk')
# Display the probability mass function (``pmf``):
x = np.arange(zipf.ppf(0.01, a), zipf.ppf(0.99, a))
ax.plot(x, zipf.pmf(x, a), 'bo', ms=8, label='zipf pmf')
ax.vlines(x, 0, zipf.pmf(x, a), colors='b', lw=5, alpha=0.5)
# Alternatively, the distribution object can be called (as a function)
# to fix the shape and location. This returns a "frozen" RV object holding
# the given parameters fixed.
# Freeze the distribution and display the frozen ``pmf``:
rv = zipf(a)
ax.vlines(x,
0,
rv.pmf(x),
colors='k',
linestyles='-',
lw=1,
label='frozen pmf')
ax.legend(loc='best', frameon=False)