def ks_2samp2(data1, data2):
""" Computes the Kolmogorov-Smirnof statistic on 2 samples.
"""
data1, data2 = map(asarray, (data1, data2))
print data1
n1 = data1.shape[0]
n2 = data2.shape[0]
print n1,n2
n1 = len(data1)
n2 = len(data2)
print n1,n2
data1 = np.sort(data1)
data2 = np.sort(data2)
print data1
data_all = np.concatenate([data1,data2])
#print data_all
cdf1 = np.searchsorted(data1,data_all,side='right')/(1.0*n1)
print cdf1
cdf2 = (np.searchsorted(data2,data_all,side='right'))/(1.0*n2)
d = np.max(np.absolute(cdf1-cdf2))
#Note: d absolute not signed distance
en = np.sqrt(n1*n2/float(n1+n2))
try:
prob = ksprob((en+0.12+0.11/en)*d)
except:
prob = 1.0
return d, prob
def ks_2samp(data1, data2):
"""
Computes the Kolmogorov-Smirnof statistic on 2 samples.
This is a two-sided test for the null hypothesis that 2 independent samples
are drawn from the same continuous distribution.
TAK: taken from scipy.stats. Extended to return the value for which
the KS-statistic is maximal.
Parameters
----------
a, b : sequence of 1-D ndarrays
two arrays of sample observations assumed to be drawn from a continuous
distribution, sample sizes can be different
Returns
-------
D : float
KS statistic
p-value : float
two-tailed p-value
x_D: float
value of the control-variable for which the KS statistic is maximal
Notes
-----
This tests whether 2 samples are drawn from the same distribution. Note
that, like in the case of the one-sample K-S test, the distribution is
assumed to be continuous.
This is the two-sided test, one-sided tests are not implemented.
The test uses the two-sided asymptotic Kolmogorov-Smirnov distribution.
If the K-S statistic is small or the p-value is high, then we cannot
reject the hypothesis that the distributions of the two samples
are the same.
Examples
--------
>>> from scipy import stats
>>> import numpy as np
>>> from scipy.stats import ks_2samp
>>> #fix random seed to get the same result
>>> np.random.seed(12345678);
>>> n1 = 200 # size of first sample
>>> n2 = 300 # size of second sample
different distribution
we can reject the null hypothesis since the pvalue is below 1%
>>> rvs1 = stats.norm.rvs(size=n1,loc=0.,scale=1);
>>> rvs2 = stats.norm.rvs(size=n2,loc=0.5,scale=1.5)
>>> ks_2samp(rvs1,rvs2)
(0.20833333333333337, 4.6674975515806989e-005)
slightly different distribution
we cannot reject the null hypothesis at a 10% or lower alpha since
the pvalue at 0.144 is higher than 10%
>>> rvs3 = stats.norm.rvs(size=n2,loc=0.01,scale=1.0)
>>> ks_2samp(rvs1,rvs3)
(0.10333333333333333, 0.14498781825751686)
identical distribution
we cannot reject the null hypothesis since the pvalue is high, 41%
>>> rvs4 = stats.norm.rvs(size=n2,loc=0.0,scale=1.0)
>>> ks_2samp(rvs1,rvs4)
(0.07999999999999996, 0.41126949729859719)
"""
data1, data2 = map(np.asarray, (data1, data2))
n1 = data1.shape[0]
n2 = data2.shape[0]
n1 = len(data1)
n2 = len(data2)
data1 = np.sort(data1)
data2 = np.sort(data2)
data_all = np.concatenate([data1,data2])
cdf1 = np.searchsorted(data1,data_all,side='right')/(1.0*n1)
cdf2 = (np.searchsorted(data2,data_all,side='right'))/(1.0*n2)
d = np.max(np.absolute(cdf1-cdf2))
x_d = data_all[np.argmax(np.absolute(cdf1-cdf2))]
#Note: d absolute not signed distance
en = np.sqrt(n1*n2/float(n1+n2))
try:
prob = ksprob((en+0.12+0.11/en)*d)
except:
prob = 1.0
return d, prob, x_d
def err(p, fp_ref):
#print p,fp_ref
#print "p, fp_ref:", p, fp_ref
return abs(fp_ref - ksprob((en + 0.12 + 0.11 / en) * p[0]))
print "cdfa:"
print cdfa
print "cdfb:"
print cdfb
print "cdfa-cdfb"
print cdfa - cdfb
d = np.max(np.absolute(cdfa-cdfb))
#Note: d absolute not signed distance
en = np.sqrt(na*nb/float(na+nb))
print en
try:
#prob = ksprob((en+0.12+0.11/en)*d)
prob = ksprob(d*en)
except:
prob = 1.0
print d, prob
print ksprob(0.2)
print ksprob(0.4)
print ksprob(0.6)
print ksprob(0.8)
def err(p,fp_ref):
#print p,fp_ref
#print "p, fp_ref:", p, fp_ref
return abs(fp_ref-ksprob((en+0.12+0.11/en)*p[0]))
def ks_2samp(data1, data2):
"""
Computes the Kolmogorov-Smirnof statistic on 2 samples.
This is a two-sided test for the null hypothesis that 2 independent samples
are drawn from the same continuous distribution.
TAK: taken from scipy.stats. Extended to return the value for which
the KS-statistic is maximal.
Parameters
----------
a, b : sequence of 1-D ndarrays
two arrays of sample observations assumed to be drawn from a continuous
distribution, sample sizes can be different
Returns
-------
D : float
KS statistic
p-value : float
two-tailed p-value
x_D: float
value of the control-variable for which the KS statistic is maximal
Notes
-----
This tests whether 2 samples are drawn from the same distribution. Note
that, like in the case of the one-sample K-S test, the distribution is
assumed to be continuous.
This is the two-sided test, one-sided tests are not implemented.
The test uses the two-sided asymptotic Kolmogorov-Smirnov distribution.
If the K-S statistic is small or the p-value is high, then we cannot
reject the hypothesis that the distributions of the two samples
are the same.
Examples
--------
>>> from scipy import stats
>>> import numpy as np
>>> from scipy.stats import ks_2samp
>>> #fix random seed to get the same result
>>> np.random.seed(12345678);
>>> n1 = 200 # size of first sample
>>> n2 = 300 # size of second sample
different distribution
we can reject the null hypothesis since the pvalue is below 1%
>>> rvs1 = stats.norm.rvs(size=n1,loc=0.,scale=1);
>>> rvs2 = stats.norm.rvs(size=n2,loc=0.5,scale=1.5)
>>> ks_2samp(rvs1,rvs2)
(0.20833333333333337, 4.6674975515806989e-005)
slightly different distribution
we cannot reject the null hypothesis at a 10% or lower alpha since
the pvalue at 0.144 is higher than 10%
>>> rvs3 = stats.norm.rvs(size=n2,loc=0.01,scale=1.0)
>>> ks_2samp(rvs1,rvs3)
(0.10333333333333333, 0.14498781825751686)
identical distribution
we cannot reject the null hypothesis since the pvalue is high, 41%
>>> rvs4 = stats.norm.rvs(size=n2,loc=0.0,scale=1.0)
>>> ks_2samp(rvs1,rvs4)
(0.07999999999999996, 0.41126949729859719)
"""
data1, data2 = map(np.asarray, (data1, data2))
n1 = data1.shape[0]
n2 = data2.shape[0]
n1 = len(data1)
n2 = len(data2)
data1 = np.sort(data1)
data2 = np.sort(data2)
data_all = np.concatenate([data1, data2])
cdf1 = np.searchsorted(data1, data_all, side="right") / (1.0 * n1)
cdf2 = (np.searchsorted(data2, data_all, side="right")) / (1.0 * n2)
d = np.max(np.absolute(cdf1 - cdf2))
x_d = data_all[np.argmax(np.absolute(cdf1 - cdf2))]
# Note: d absolute not signed distance
en = np.sqrt(n1 * n2 / float(n1 + n2))
try:
prob = ksprob((en + 0.12 + 0.11 / en) * d)
except:
prob = 1.0
return d, prob, x_d
def ks_2samp(data1, data2, signed=False):
"""
Computes the Kolmogorov-Smirnov statistic on two samples, as well
as its two-sided p-value.
The two-sample Kolmogorov-Smirnov statistic is
D = sup_x |A(x) - B(x)|,
where A and B are the empirical distribution functions of
parameters `a` and `b`, respectively. This is a two-sided test for
the null hypothesis that two independent samples are drawn from the
same continuous distribution.
Parameters
----------
a, b : sequence of 1-D ndarrays
Two arrays of sample observations assumed to be drawn from a continuous
distribution. The sample sizes can be different.
signed : {False, True}, optional
This flag determines whether the returned value `D` should
be signed to indicate which distribution function is largest
at the point where the two distribution functions differ the most.
When `signed` is true, `D` will be
A(x) - B(x) where x = arg sup_x |A(x) - B(x)|.
With the default value, False, `D` will be sup_x |A(X) - B(x)|
and therefore always in [0, 1].
Returns
-------
D : float
KS statistic
p-value : float
two-tailed p-value
Notes
-----
This tests whether 2 samples are drawn from the same distribution. Note
that, like in the case of the one-sample K-S test, the distribution is
assumed to be continuous.
This is the two-sided test, one-sided tests are not implemented.
The test uses the two-sided asymptotic Kolmogorov-Smirnov distribution.
If the K-S statistic is small or the p-value is high, then we cannot
reject the hypothesis that the distributions of the two samples
are the same.
Examples
--------
>>> from scipy import stats
>>> import numpy as np
>>> from scipy.stats import ks_2samp
>>> #fix random seed to get the same result
>>> np.random.seed(12345678);
>>> n1 = 200 # size of first sample
>>> n2 = 300 # size of second sample
different distribution
we can reject the null hypothesis since the pvalue is below 1%
>>> rvs1 = stats.norm.rvs(size=n1,loc=0.,scale=1);
>>> rvs2 = stats.norm.rvs(size=n2,loc=0.5,scale=1.5)
>>> ks_2samp(rvs1,rvs2)
(0.20833333333333337, 4.6674975515806989e-005)
slightly different distribution
we cannot reject the null hypothesis at a 10% or lower alpha since
the pvalue at 0.144 is higher than 10%
>>> rvs3 = stats.norm.rvs(size=n2,loc=0.01,scale=1.0)
>>> ks_2samp(rvs1,rvs3)
(0.10333333333333333, 0.14498781825751686)
identical distribution
we cannot reject the null hypothesis since the pvalue is high, 41%
>>> rvs4 = stats.norm.rvs(size=n2,loc=0.0,scale=1.0)
>>> ks_2samp(rvs1,rvs4)
(0.07999999999999996, 0.41126949729859719)
When `signed` is true, the KS-statistic will be negative if the
second distribution function is the largest at the point where the
distribution functions differ the most.
>>> ks_2samp(rvs1,rvs4,signed=True)
(-0.07999999999999996, 0.41126949729859719)
"""
data1, data2 = map(asarray, (data1, data2))
n1 = data1.shape[0]
n2 = data2.shape[0]
n1 = len(data1)
n2 = len(data2)
data1 = np.sort(data1)
data2 = np.sort(data2)
data_all = np.concatenate([data1,data2])
cdf1 = np.searchsorted(data1,data_all,side='right')/(1.0*n1)
cdf2 = (np.searchsorted(data2,data_all,side='right'))/(1.0*n2)
diff = cdf1-cdf2
ind = np.argmax(np.absolute(diff))
d = diff[ind]
absd = np.absolute(d)
en = np.sqrt(n1*n2/float(n1+n2))
try:
prob = ksprob((en+0.12+0.11/en)*absd)
except:
prob = 1.0
if signed:
return d, prob
else:
return absd, prob
def ks_2samp(data1, data2, signed=False):
"""
Computes the Kolmogorov-Smirnov statistic on two samples, as well
as its two-sided p-value.
The two-sample Kolmogorov-Smirnov statistic is
D = sup_x |A(x) - B(x)|,
where A and B are the empirical distribution functions of
parameters `a` and `b`, respectively. This is a two-sided test for
the null hypothesis that two independent samples are drawn from the
same continuous distribution.
Parameters
----------
a, b : sequence of 1-D ndarrays
Two arrays of sample observations assumed to be drawn from a continuous
distribution. The sample sizes can be different.
signed : {False, True}, optional
This flag determines whether the returned value `D` should
be signed to indicate which distribution function is largest
at the point where the two distribution functions differ the most.
When `signed` is true, `D` will be
A(x) - B(x) where x = arg sup_x |A(x) - B(x)|.
With the default value, False, `D` will be sup_x |A(X) - B(x)|
and therefore always in [0, 1].
Returns
-------
D : float
KS statistic
p-value : float
two-tailed p-value
Notes
-----
This tests whether 2 samples are drawn from the same distribution. Note
that, like in the case of the one-sample K-S test, the distribution is
assumed to be continuous.
This is the two-sided test, one-sided tests are not implemented.
The test uses the two-sided asymptotic Kolmogorov-Smirnov distribution.
If the K-S statistic is small or the p-value is high, then we cannot
reject the hypothesis that the distributions of the two samples
are the same.
Examples
--------
>>> from scipy import stats
>>> import numpy as np
>>> from scipy.stats import ks_2samp
>>> #fix random seed to get the same result
>>> np.random.seed(12345678);
>>> n1 = 200 # size of first sample
>>> n2 = 300 # size of second sample
different distribution
we can reject the null hypothesis since the pvalue is below 1%
>>> rvs1 = stats.norm.rvs(size=n1,loc=0.,scale=1);
>>> rvs2 = stats.norm.rvs(size=n2,loc=0.5,scale=1.5)
>>> ks_2samp(rvs1,rvs2)
(0.20833333333333337, 4.6674975515806989e-005)
slightly different distribution
we cannot reject the null hypothesis at a 10% or lower alpha since
the pvalue at 0.144 is higher than 10%
>>> rvs3 = stats.norm.rvs(size=n2,loc=0.01,scale=1.0)
>>> ks_2samp(rvs1,rvs3)
(0.10333333333333333, 0.14498781825751686)
identical distribution
we cannot reject the null hypothesis since the pvalue is high, 41%
>>> rvs4 = stats.norm.rvs(size=n2,loc=0.0,scale=1.0)
>>> ks_2samp(rvs1,rvs4)
(0.07999999999999996, 0.41126949729859719)
When `signed` is true, the KS-statistic will be negative if the
second distribution function is the largest at the point where the
distribution functions differ the most.
>>> ks_2samp(rvs1,rvs4,signed=True)
(-0.07999999999999996, 0.41126949729859719)
"""
data1, data2 = map(asarray, (data1, data2))
n1 = data1.shape[0]
n2 = data2.shape[0]
n1 = len(data1)
n2 = len(data2)
data1 = np.sort(data1)
data2 = np.sort(data2)
data_all = np.concatenate([data1, data2])
cdf1 = np.searchsorted(data1, data_all, side='right') / (1.0 * n1)
cdf2 = (np.searchsorted(data2, data_all, side='right')) / (1.0 * n2)
diff = cdf1 - cdf2
ind = np.argmax(np.absolute(diff))
d = diff[ind]
absd = np.absolute(d)
en = np.sqrt(n1 * n2 / float(n1 + n2))
try:
prob = ksprob((en + 0.12 + 0.11 / en) * absd)
except:
prob = 1.0
if signed:
return d, prob
else:
return absd, prob
