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
mc, mnc = mvsk2m(dmvsk)
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 __init__(self, args, **kwds):
# todo: replace with super call
distributions.rv_continuous.__init__(
self,
name="Normal Expansion distribution",
shapes="alpha",
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)
