def test_hotelling4():
# Hotelling T^2 should just be like taking product with sphere.
x = np.linspace(0.1,10,100)
for dim in range(7):
search = rft.IntrinsicVolumes([0]*(dim) + [1])
for k in range(5, 10):
p = rft.spherical_search(k)
for dfd in [np.inf,40,50]:
f = rft.FStat(dfd=dfd, dfn=1)(x, search=p*search)
t = 2*rft.TStat(dfd=dfd)(np.sqrt(x), search=p*search)
h2 = 2*rft.Hotelling(k=k, dfd=dfd).density(x, dim)
h = 2*rft.Hotelling(k=k, dfd=dfd)(x, search=search)
yield assert_almost_equal, h, t
yield assert_almost_equal, h, f
yield assert_almost_equal, h, h2
search = rft.IntrinsicVolumes([3,4,5])
for k in range(5, 10):
p = rft.spherical_search(k)
for dfd in [np.inf,40,50]:
f = rft.FStat(dfd=dfd, dfn=1)(x, search=p*search)
h = 2*rft.Hotelling(k=k, dfd=dfd)(x, search=search)
h2 = 0
for i in range(search.mu.shape[0]):
h2 += 2*rft.Hotelling(k=k, dfd=dfd).density(x, i) * search.mu[i]
yield assert_almost_equal, h, f
yield assert_almost_equal, h, h2
def test_hotelling2():
# Marginally, Hotelling's T^2(k) with m degrees of freedom
# in the denominator satisfies
# (m-k+1)/(mk) T^2 \sim F_{k,m-k+1}.
x = np.linspace(0.1, 10, 100)
for dfn in range(6, 10):
h = rft.Hotelling(k=dfn)(x)
chi = rft.ChiSquared(dfn=dfn)(x)
assert_almost_equal(h, chi)
chi2 = scipy.stats.chi2.sf(x, dfn)
yield assert_almost_equal, h, chi2
p = rft.spherical_search(dfn)
for dfd in [40, 50]:
fac = (dfd - dfn + 1.0) / (dfd * dfn)
h = rft.Hotelling(dfd=dfd, k=dfn)(x)
f = scipy.stats.f.sf(x * fac, dfn, dfd - dfn + 1)
f2 = rft.FStat(dfd=dfd - dfn + 1, dfn=dfn)(x * fac)
yield assert_almost_equal, f2, f
yield assert_almost_equal, h, f
