def test_zipfian_continuity(self):
# test that zipfian(0.999999, n) ~ zipfian(1.000001, n)
# (a = 1 switches between methods of calculating harmonic sum)
alt1, agt1 = 0.99999999, 1.00000001
N = 30
k = np.arange(1, N + 1)
assert_allclose(zipfian.pmf(k, alt1, N), zipfian.pmf(k, agt1, N))
assert_allclose(zipfian.cdf(k, alt1, N), zipfian.cdf(k, agt1, N))
assert_allclose(zipfian.sf(k, alt1, N), zipfian.sf(k, agt1, N))
assert_allclose(zipfian.stats(alt1, N, moments='msvk'),
zipfian.stats(agt1, N, moments='msvk'), rtol=2e-7)
def test_zipfian_naive(self, a, n):
# test against bare-bones implementation
@np.vectorize
def Hns(n, s):
"""Naive implementation of harmonic sum"""
return (1 / np.arange(1, n + 1)**s).sum()
@np.vectorize
def pzip(k, a, n):
"""Naive implementation of zipfian pmf"""
if k < 1 or k > n:
return 0.
else:
return 1 / k**a / Hns(n, a)
k = np.arange(n + 1)
pmf = pzip(k, a, n)
cdf = np.cumsum(pmf)
mean = np.average(k, weights=pmf)
var = np.average((k - mean)**2, weights=pmf)
std = var**0.5
skew = np.average(((k - mean) / std)**3, weights=pmf)
kurtosis = np.average(((k - mean) / std)**4, weights=pmf) - 3
assert_allclose(zipfian.pmf(k, a, n), pmf)
assert_allclose(zipfian.cdf(k, a, n), cdf)
assert_allclose(zipfian.stats(a, n, moments="mvsk"),
[mean, var, skew, kurtosis])
def test_zipfian_R(self):
# test against R VGAM package
# library(VGAM)
# k <- c(13, 16, 1, 4, 4, 8, 10, 19, 5, 7)
# a <- c(1.56712977, 3.72656295, 5.77665117, 9.12168729, 5.79977172,
# 4.92784796, 9.36078764, 4.3739616 , 7.48171872, 4.6824154)
# n <- c(70, 80, 48, 65, 83, 89, 50, 30, 20, 20)
# pmf <- dzipf(k, N = n, shape = a)
# cdf <- pzipf(k, N = n, shape = a)
# print(pmf)
# print(cdf)
np.random.seed(0)
k = np.random.randint(1, 20, size=10)
a = np.random.rand(10) * 10 + 1
n = np.random.randint(1, 100, size=10)
pmf = [
8.076972e-03, 2.950214e-05, 9.799333e-01, 3.216601e-06,
3.158895e-04, 3.412497e-05, 4.350472e-10, 2.405773e-06,
5.860662e-06, 1.053948e-04
]
cdf = [
0.8964133, 0.9998666, 0.9799333, 0.9999995, 0.9998584, 0.9999458,
1.0000000, 0.9999920, 0.9999977, 0.9998498
]
# skip the first point; zipUC is not accurate for low a, n
assert_allclose(zipfian.pmf(k, a, n)[1:], pmf[1:], rtol=1e-6)
assert_allclose(zipfian.cdf(k, a, n)[1:], cdf[1:], rtol=5e-5)
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'))
