'''More Goodness of fit tests

contains

GOF : 1 sample gof tests based on Stephens 1970, plus AD A^2
bootstrap : vectorized bootstrap p-values for gof test with fitted parameters


Created : 2011-05-21
Author : Josef Perktold

parts based on ks_2samp and kstest from scipy.stats
(license: Scipy BSD, but were completely rewritten by Josef Perktold)


References
----------

'''
from __future__ import print_function
from statsmodels.compat.python import range, lmap, string_types, callable
import numpy as np

from scipy.stats import distributions

from statsmodels.tools.decorators import cache_readonly

from scipy.special import kolmogorov as ksprob

#from scipy.stats unchanged
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.

    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


    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 = lmap(np.asarray, (data1, data2))
    n1 = data1.shape[0]
    n2 = data2.shape[0]
    n1 = len(data1)
    n2 = len(data2)
    data1 = np.sort(data1)