def summary(self, yname=None, xname=None, title=None, alpha=0.05):
df = pd.DataFrame()
df["Type"] = (["Mean"] * self.k_exog + ["Scale"] * self.k_scale +
["Smooth"] * self.k_smooth + ["SD"] * self.k_noise)
df["coef"] = self.params
try:
df["std err"] = np.sqrt(np.diag(self.cov_params()))
except Exception:
df["std err"] = np.nan
from scipy.stats.distributions import norm
df["tvalues"] = df.coef / df["std err"]
df["P>|t|"] = 2 * norm.sf(np.abs(df.tvalues))
f = norm.ppf(1 - alpha / 2)
df["[%.3f" % (alpha / 2)] = df.coef - f * df["std err"]
df["%.3f]" % (1 - alpha / 2)] = df.coef + f * df["std err"]
df.index = self.model.data.param_names
summ = summary2.Summary()
if title is None:
title = "Gaussian process regression results"
summ.add_title(title)
summ.add_df(df)
return summ
def mannwhitneyu(x, y, use_continuity=True):
"""
Computes the Mann-Whitney rank test on samples x and y.
Parameters
----------
x, y : array_like
Array of samples, should be one-dimensional.
use_continuity : bool, optional
Whether a continuity correction (1/2.) should be taken into
account. Default is True.
Returns
-------
u : float
The Mann-Whitney statistics.
prob : float
One-sided p-value assuming a asymptotic normal distribution.
Notes
-----
Use only when the number of observation in each sample is > 20 and
you have 2 independent samples of ranks. Mann-Whitney U is
significant if the u-obtained is LESS THAN or equal to the critical
value of U.
This test corrects for ties and by default uses a continuity correction.
The reported p-value is for a one-sided hypothesis, to get the two-sided
p-value multiply the returned p-value by 2.
"""
x = np.asarray(x)
y = np.asarray(y)
n1 = len(x)
n2 = len(y)
ranked = rankdata(np.concatenate((x,y)))
rankx = ranked[0:n1] # get the x-ranks
#ranky = ranked[n1:] # the rest are y-ranks
u1 = n1*n2 + (n1*(n1+1))/2.0 - np.sum(rankx,axis=0) # calc U for x
u2 = n1*n2 - u1 # remainder is U for y
bigu = max(u1,u2)
smallu = min(u1,u2)
#T = np.sqrt(tiecorrect(ranked)) # correction factor for tied scores
T = tiecorrect(ranked)
if T == 0:
raise ValueError('All numbers are identical in amannwhitneyu')
sd = np.sqrt(T*n1*n2*(n1+n2+1)/12.0)
if use_continuity:
# normal approximation for prob calc with continuity correction
z = (bigu-0.5-n1*n2/2.0) / sd
else:
z = (bigu-n1*n2/2.0) / sd # normal approximation for prob calc
z *= int(u1<u2)-int(u1>u2)
return z, norm.sf(abs(z)) #(1.0 - zprob(z))
def mannwhitneyu(self, x, y, use_continuity=True):
x = asarray(x)
y = asarray(y)
n1 = len(x)
n2 = len(y)
ranked = rankdata(np.concatenate((x, y)))
rankx = ranked[0:n1] # get the x-ranks
u1 = n1 * n2 + (n1 * (n1 + 1)) / 2.0 - np.sum(rankx, axis=0) # calc U for x
u2 = n1 * n2 - u1 # remainder is U for y
bigu = max(u1, u2)
smallu = min(u1, u2)
T = tiecorrect(ranked)
sd = np.sqrt(T * n1 * n2 * (n1 + n2 + 1) / 12.0)
if use_continuity:
# normal approximation for prob calc with continuity correction
z = abs((bigu - 0.5 - n1 * n2 / 2.0) / sd)
else:
z = abs((bigu - n1 * n2 / 2.0) / sd) # normal approximation for prob calc
p = norm.sf(z)
return smallu, bigu, z, p
