#### Previous topic

scipy.stats.skewtest

#### Next topic

scipy.stats.kstatvar

# scipy.stats.kstat

`scipy.stats.``kstat`(data, n=2)

  Return the nth k-statistic (1<=n<=4 so far).

  The nth k-statistic is the unique symmetric unbiased estimator of the nth cumulant kappa_n.

  Parameters: | data : array_like Input array. n : int, {1, 2, 3, 4}, optional Default is equal to 2.
  Returns: | kstat : float The nth k-statistic.

  See also

  `kstatvar`
    Returns an unbiased estimator of the variance of the k-statistic.

  Notes

  The cumulants are related to central moments but are specifically defined using a power series expansion of the logarithm of the characteristic function (which is the Fourier transform of the PDF). In particular let phi(t) be the characteristic function, then:

      ln phi(t) = > kappa_n (it)^n / n!    (sum from n=0 to inf)

  The first few cumulants (kappa_n) in terms of central moments (mu_n) are:

      kappa_1 = mu_1
      kappa_2 = mu_2
      kappa_3 = mu_3
      kappa_4 = mu_4 - 3*mu_2**2
      kappa_5 = mu_5 - 10*mu_2 * mu_3

  References

  http://mathworld.wolfram.com/k-Statistic.html

  http://mathworld.wolfram.com/Cumulant.html