code: def _mover_confint(stat1, stat2, ci1, ci2, contrast="diff"):
      """
  
      References
      ----------
  
      .. [#] Krishnamoorthy, K., Jie Peng, and Dan Zhang. 2016. “Modified Large
         Sample Confidence Intervals for Poisson Distributions: Ratio, Weighted
         Average, and Product of Means.” Communications in Statistics - Theory
         and Methods 45 (1): 83–97. https://doi.org/10.1080/03610926.2013.821486.
  
  
      .. [#] Li, Yanhong, John J. Koval, Allan Donner, and G. Y. Zou. 2010.
         “Interval Estimation for the Area under the Receiver Operating
         Characteristic Curve When Data Are Subject to Error.” Statistics in
         Medicine 29 (24): 2521–31. https://doi.org/10.1002/sim.4015.
  
      .. [#] Zou, G. Y., and A. Donner. 2008. “Construction of Confidence Limits
         about Effect Measures: A General Approach.” Statistics in Medicine 27
         (10): 1693–1702. https://doi.org/10.1002/sim.3095.
      """
  
      if contrast == "diff":
          stat = stat1 - stat2
          low_half = np.sqrt(
              (stat1 - ci1[0]) ** 2 + (stat2 - ci2[1]) ** 2
          )
          upp_half = np.sqrt(
              (stat1 - ci1[1]) ** 2 + (stat2 - ci2[0]) ** 2
          )
          ci = (stat - low_half, stat + upp_half)
  
      elif contrast == "sum":
          stat = stat1 + stat2
          low_half = np.sqrt(
              (stat1 - ci1[0]) ** 2 + (stat2 - ci2[0]) ** 2
          )
          upp_half = np.sqrt(
              (stat1 - ci1[1]) ** 2 + (stat2 - ci2[1]) ** 2
          )
          ci = (stat - low_half, stat + upp_half)
  
      elif contrast == "ratio":
          # stat = stat1 / stat2
          prod = stat1 * stat2
          term1 = stat2**2 - (ci2[1] - stat2) ** 2
          term2 = stat2**2 - (ci2[0] - stat2) ** 2
          low_ = (
              prod
              - np.sqrt(
                  prod**2
                  - term1 * (stat1**2 - (ci1[0] - stat1) ** 2)
              )
          ) / term1
          upp_ = (
              prod
              + np.sqrt(
                  prod**2
                  - term2 * (stat1**2 - (ci1[1] - stat1) ** 2)
              )
          ) / term2
  
          # method 2 Li, Tang, Wong 2014
          low1, upp1 = ci1
          low2, upp2 = ci2
          term1 = upp2 * (2 * stat2 - upp2)
          term2 = low2 * (2 * stat2 - low2)
          low = (
              prod
              - np.sqrt(prod**2 - term1 * low1 * (2 * stat1 - low1))
          ) / term1
          upp = (
              prod
              + np.sqrt(prod**2 - term2 * upp1 * (2 * stat1 - upp1))
          ) / term2
  
          assert_allclose(
              (low_, upp_), (low, upp), atol=1e-15, rtol=1e-10
          )
  
          ci = (low, upp)
  
      return ci
  
imports: import numpy
  from numpy.testing import assert_allclose
label_desc: Use image node_id 1 for calling a global function with example usage: _mover_confint(stat1, stat2, ci1, ci2, contrast) and returns: ci