from scipy.stats import nbinom
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)

# Calculate a few first moments:

n, p = 0.4, 0.4
mean, var, skew, kurt = nbinom.stats(n, p, moments='mvsk')

# Display the probability mass function (``pmf``):

x = np.arange(nbinom.ppf(0.01, n, p),
              nbinom.ppf(0.99, n, p))
ax.plot(x, nbinom.pmf(x, n, p), 'bo', ms=8, label='nbinom pmf')
ax.vlines(x, 0, nbinom.pmf(x, n, p), 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 = nbinom(n, p)
ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1,
        label='frozen pmf')
ax.legend(loc='best', frameon=False)
plt.show()

# Check accuracy of ``cdf`` and ``ppf``:

prob = nbinom.cdf(x, n, p)
np.allclose(x, nbinom.ppf(prob, n, p))
# True

# Generate random numbers:

r = nbinom.rvs(n, p, size=1000)