code: def expected_robust_kurtosis(ab=(5.0, 50.0), dg=(2.5, 25.0)):
      """
      Calculates the expected value of the robust kurtosis measures in Kim and
      White assuming the data are normally distributed.
  
      Parameters
      ----------
      ab : iterable, optional
          Contains 100*(alpha, beta) in the kr3 measure where alpha is the tail
          quantile cut-off for measuring the extreme tail and beta is the central
          quantile cutoff for the standardization of the measure
      db : iterable, optional
          Contains 100*(delta, gamma) in the kr4 measure where delta is the tail
          quantile for measuring extreme values and gamma is the central quantile
          used in the the standardization of the measure
  
      Returns
      -------
      ekr : ndarray, 4-element
          Contains the expected values of the 4 robust kurtosis measures
  
      Notes
      -----
      See `robust_kurtosis` for definitions of the robust kurtosis measures
      """
  
      alpha, beta = ab
      delta, gamma = dg
      expected_value = np.zeros(4)
      ppf = stats.norm.ppf
      pdf = stats.norm.pdf
      q1, q2, q3, q5, q6, q7 = ppf(
          np.array((1.0, 2.0, 3.0, 5.0, 6.0, 7.0)) / 8
      )
      expected_value[0] = 3
  
      expected_value[1] = ((q7 - q5) + (q3 - q1)) / (q6 - q2)
  
      q_alpha, q_beta = ppf(np.array((alpha / 100.0, beta / 100.0)))
      expected_value[2] = (2 * pdf(q_alpha) / alpha) / (
          2 * pdf(q_beta) / beta
      )
  
      q_delta, q_gamma = ppf(np.array((delta / 100.0, gamma / 100.0)))
      expected_value[3] = (-2.0 * q_delta) / (-2.0 * q_gamma)
  
      return expected_value
  
file_path: statsmodels/statsmodels/stats/stattools.py
imports: from scipy import stats
  import numpy
  from statsmodels.tools.sm_exceptions import ValueWarning
label_desc: Use image node_id 6 for calling a global function with example usage: expected_robust_kurtosis(ab, dg) and returns: expected_value