This is documentation for an old release of SciPy (version 0.17.1). Read this page in the documentation of the latest stable release (version 1.15.0).
scipy.stats.kstat¶
- scipy.stats.kstat(data, n=2)[source]¶
Return the nth k-statistic (1<=n<=4 so far).
The nth k-statistic k_n is the unique symmetric unbiased estimator of the nth cumulant kappa_n.
Parameters: data : array_like
Input array. Note that n-D input gets flattened.
n : int, {1, 2, 3, 4}, optional
Default is equal to 2.
Returns: kstat : float
The nth k-statistic.
See also
Notes
For a sample size n, the first few k-statistics are given by:
k1=μk2=nn−1m2k3=n2(n−1)(n−2)m3k4=n2[(n+1)m4−3(n−1)m22](n−1)(n−2)(n−3)where :math:\mu is the sample mean, :math:m_2 is the sample variance, and :math:m_i is the i-th sample central moment.
References
http://mathworld.wolfram.com/k-Statistic.html
http://mathworld.wolfram.com/Cumulant.html
Examples
>>> from scipy import stats >>> rndm = np.random.RandomState(1234)
As sample size increases, n-th moment and n-th k-statistic converge to the same number (although they aren’t identical). In the case of the normal distribution, they converge to zero.
>>> for n in [2, 3, 4, 5, 6, 7]: ... x = rndm.normal(size=10**n) ... m, k = stats.moment(x, 3), stats.kstat(x, 3) ... print("%.3g %.3g %.3g" % (m, k, m-k)) -0.631 -0.651 0.0194 0.0282 0.0283 -8.49e-05 -0.0454 -0.0454 1.36e-05 7.53e-05 7.53e-05 -2.26e-09 0.00166 0.00166 -4.99e-09 -2.88e-06 -2.88e-06 8.63e-13