def examples_normexpand():
skewnorm = SkewNorm_gen()
rvs = skewnorm.rvs(5, size=100)
normexpan = NormExpan_gen(rvs, mode='sample')
smvsk = stats.describe(rvs)[2:]
print 'sample: mu,sig,sk,kur'
print smvsk
dmvsk = normexpan.stats(moments='mvsk')
print 'normexpan: mu,sig,sk,kur'
print dmvsk
print 'mvsk diff distribution - sample'
print np.array(dmvsk) - np.array(smvsk)
print 'normexpan attributes mvsk'
print mc2mvsk(normexpan.cnt)
print normexpan.mvsk
from statsmodels.stats.momenthelpers import mvsk2mnc, mnc2mc
mnc = mvsk2mnc(dmvsk)
mc = mnc2mc(mnc)
print 'central moments'
print mc
print 'non-central moments'
print mnc
pdffn = pdf_moments(mc)
print '\npdf approximation from moments'
print 'pdf at', mc[0] - 1, mc[0] + 1
print pdffn([mc[0] - 1, mc[0] + 1])
print normexpan.pdf([mc[0] - 1, mc[0] + 1])
def examples_normexpand():
skewnorm = SkewNorm_gen()
rvs = skewnorm.rvs(5,size=100)
normexpan = NormExpan_gen(rvs, mode='sample')
smvsk = stats.describe(rvs)[2:]
print 'sample: mu,sig,sk,kur'
print smvsk
dmvsk = normexpan.stats(moments='mvsk')
print 'normexpan: mu,sig,sk,kur'
print dmvsk
print 'mvsk diff distribution - sample'
print np.array(dmvsk) - np.array(smvsk)
print 'normexpan attributes mvsk'
print mc2mvsk(normexpan.cnt)
print normexpan.mvsk
from statsmodels.stats.momenthelpers import mvsk2mnc, mnc2mc
mnc = mvsk2mnc(dmvsk)
mc = mnc2mc(mnc)
print 'central moments'
print mc
print 'non-central moments'
print mnc
pdffn = pdf_moments(mc)
print '\npdf approximation from moments'
print 'pdf at', mc[0]-1,mc[0]+1
print pdffn([mc[0]-1,mc[0]+1])
print normexpan.pdf([mc[0]-1,mc[0]+1])
def examples_normexpand():
skewnorm = SkewNorm_gen()
rvs = skewnorm.rvs(5, size=100)
normexpan = NormExpan_gen(rvs, mode='sample')
smvsk = stats.describe(rvs)[2:]
print('sample: mu,sig,sk,kur')
print(smvsk)
dmvsk = normexpan.stats(moments='mvsk')
print('normexpan: mu,sig,sk,kur')
print(dmvsk)
print('mvsk diff distribution - sample')
print(np.array(dmvsk) - np.array(smvsk))
print('normexpan attributes mvsk')
print(mc2mvsk(normexpan.cnt))
print(normexpan.mvsk)
mnc = mvsk2mnc(dmvsk)
mc = mnc2mc(mnc)
print('central moments')
print(mc)
print('non-central moments')
print(mnc)
pdffn = pdf_moments(mc)
print('\npdf approximation from moments')
print('pdf at', mc[0] - 1, mc[0] + 1)
print(pdffn([mc[0] - 1, mc[0] + 1]))
print(normexpan.pdf([mc[0] - 1, mc[0] + 1]))
def test_moment_conversion(mom):
# this was initially written for an old version of moment_helpers
# I'm not sure whether there are not redundant cases after moving functions
# test moment -> cumulant
assert_equal(mnc2cum(mc2mnc(mom[0])), mom[1])
assert_equal(mnc2cum(mom[0]), mom[2])
if len(mom) <= 4:
assert_equal(mc2cum(mom[0]), mom[1])
# test cumulant -> moment
assert_equal(cum2mc(mom[1]), mom[0])
assert_equal(mc2mnc(cum2mc(mom[2])), mom[0])
if len(mom) <= 4:
assert_equal(cum2mc(mom[1]), mom[0])
# round trip: mnc -> cum -> mc == mnc -> mc,
assert_equal(cum2mc(mnc2cum(mom[0])), mnc2mc(mom[0]))
# round trip: mc -> mnc -> mc == mc,
assert_equal(mc2mnc(mnc2mc(mom[0])), mom[0])
if len(mom[0]) == 4:
# round trip: mc -> mvsk -> mc == mc
assert_equal(mvsk2mc(mc2mvsk(mom[0])), mom[0])
def examples_normexpand():
skewnorm = SkewNorm_gen()
rvs = skewnorm.rvs(5,size=100)
normexpan = NormExpan_gen(rvs, mode='sample')
smvsk = stats.describe(rvs)[2:]
print('sample: mu,sig,sk,kur')
print(smvsk)
dmvsk = normexpan.stats(moments='mvsk')
print('normexpan: mu,sig,sk,kur')
print(dmvsk)
print('mvsk diff distribution - sample')
print(np.array(dmvsk) - np.array(smvsk))
print('normexpan attributes mvsk')
print(mc2mvsk(normexpan.cnt))
print(normexpan.mvsk)
mnc = mvsk2mnc(dmvsk)
mc = mnc2mc(mnc)
print('central moments')
print(mc)
print('non-central moments')
print(mnc)
pdffn = pdf_moments(mc)
print('\npdf approximation from moments')
print('pdf at', mc[0]-1,mc[0]+1)
print(pdffn([mc[0]-1,mc[0]+1]))
print(normexpan.pdf([mc[0]-1,mc[0]+1]))
def test_moment_conversion():
#this was initially written for an old version of moment_helpers
#I'm not sure whether there are not redundant cases after moving functions
ms = [( [0.0, 1, 0, 3], [0.0, 1.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0] ),
( [1.0, 1, 0, 3], [1.0, 1.0, 0.0, 0.0], [1.0, 0.0, -1.0, 6.0] ),
( [0.0, 1, 1, 3], [0.0, 1.0, 1.0, 0.0], [0.0, 1.0, 1.0, 0.0] ),
( [1.0, 1, 1, 3], [1.0, 1.0, 1.0, 0.0], [1.0, 0.0, 0.0, 2.0] ),
( [1.0, 1, 1, 4], [1.0, 1.0, 1.0, 1.0], [1.0, 0.0, 0.0, 3.0] ),
( [1.0, 2, 0, 3], [1.0, 2.0, 0.0, -9.0], [1.0, 1.0, -4.0, 9.0] ),
( [0.0, 2, 1, 3], [0.0, 2.0, 1.0, -9.0], [0.0, 2.0, 1.0, -9.0] ),
( [1.0, 0.5, 0, 3], [1.0, 0.5, 0.0, 2.25], [1.0, -0.5, 0.5, 2.25] ), #neg.variance if mnc2<mnc1
( [0.0, 0.5, 1, 3], [0.0, 0.5, 1.0, 2.25], [0.0, 0.5, 1.0, 2.25] ),
( [0.0, 1, 0, 3, 0], [0.0, 1.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0, 0.0] ),
( [1.0, 1, 0, 3, 1], [1.0, 1.0, 0.0, 0.0, 1.0], [1.0, 0.0, -1.0, 6.0, -20.0] )]
for mom in ms:
# test moment -> cumulant
assert_equal(mnc2cum(mc2mnc(mom[0])),mom[1])
assert_equal(mnc2cum(mom[0]),mom[2])
if len(mom) <= 4:
assert_equal(mc2cum(mom[0]),mom[1])
for mom in ms:
# test cumulant -> moment
assert_equal(cum2mc(mom[1]),mom[0])
assert_equal(mc2mnc(cum2mc(mom[2])),mom[0])
if len(mom) <= 4:
assert_equal(cum2mc(mom[1]),mom[0])
for mom in ms:
#round trip: mnc -> cum -> mc == mnc -> mc,
assert_equal(cum2mc(mnc2cum(mom[0])),mnc2mc(mom[0]))
for mom in ms:
#round trip: mc -> mnc -> mc == mc,
assert_equal(mc2mnc(mnc2mc(mom[0])), mom[0])
for mom in (m for m in ms if len(m) == 4):
#round trip: mc -> mvsk -> mc == mc
assert_equal(mvsk2mc(mc2mvsk(mom[0])), mom[0])
#round trip: mc -> mvsk -> mnc == mc -> mnc
assert_equal(mvsk2mnc(mc2mvsk(mom[0])), mc2mnc(mom[0]))
def __init__(self, args, **kwds):
# todo: replace with super call
distributions.rv_continuous.__init__(
self,
name="Normal Expansion distribution",
shapes=" ",
extradoc="""
The distribution is defined as the Gram-Charlier expansion of
the normal distribution using the first four moments. The pdf
is given by
pdf(x) = (1+ skew/6.0 * H(xc,3) + kurt/24.0 * H(xc,4))*normpdf(xc)
where xc = (x-mu)/sig is the standardized value of the random variable
and H(xc,3) and H(xc,4) are Hermite polynomials
Note: This distribution has to be parameterized during
initialization and instantiation, and does not have a shape
parameter after instantiation (similar to frozen distribution
except for location and scale.) Location and scale can be used
as with other distributions, however note, that they are relative
to the initialized distribution.
""",
)
# print args, kwds
mode = kwds.get("mode", "sample")
if mode == "sample":
mu, sig, sk, kur = stats.describe(args)[2:]
self.mvsk = (mu, sig, sk, kur)
cnt = mvsk2mc((mu, sig, sk, kur))
elif mode == "mvsk":
cnt = mvsk2mc(args)
self.mvsk = args
elif mode == "centmom":
cnt = args
self.mvsk = mc2mvsk(cnt)
else:
raise ValueError("mode must be 'mvsk' or centmom")
self.cnt = cnt
# self.mvsk = (mu,sig,sk,kur)
# self._pdf = pdf_moments(cnt)
self._pdf = pdf_mvsk(self.mvsk)
def __init__(self, args, **kwds):
#todo: replace with super call
distributions.rv_continuous.__init__(
self,
name='Normal Expansion distribution',
shapes=' ',
extradoc='''
The distribution is defined as the Gram-Charlier expansion of
the normal distribution using the first four moments. The pdf
is given by
pdf(x) = (1+ skew/6.0 * H(xc,3) + kurt/24.0 * H(xc,4))*normpdf(xc)
where xc = (x-mu)/sig is the standardized value of the random variable
and H(xc,3) and H(xc,4) are Hermite polynomials
Note: This distribution has to be parameterized during
initialization and instantiation, and does not have a shape
parameter after instantiation (similar to frozen distribution
except for location and scale.) Location and scale can be used
as with other distributions, however note, that they are relative
to the initialized distribution.
''')
#print args, kwds
mode = kwds.get('mode', 'sample')
if mode == 'sample':
mu, sig, sk, kur = stats.describe(args)[2:]
self.mvsk = (mu, sig, sk, kur)
cnt = mvsk2mc((mu, sig, sk, kur))
elif mode == 'mvsk':
cnt = mvsk2mc(args)
self.mvsk = args
elif mode == 'centmom':
cnt = args
self.mvsk = mc2mvsk(cnt)
else:
raise ValueError("mode must be 'mvsk' or centmom")
self.cnt = cnt
#self.mvsk = (mu,sig,sk,kur)
#self._pdf = pdf_moments(cnt)
self._pdf = pdf_mvsk(self.mvsk)
def test_multidimensional(test_vals):
assert_almost_equal(cum2mc(mnc2cum(mc2mnc(test_vals).T).T).T, test_vals)
assert_almost_equal(cum2mc(mc2cum(test_vals).T).T, test_vals)
assert_almost_equal(mvsk2mc(mc2mvsk(test_vals).T).T, test_vals)