class_docstr: Multivariate kernel density estimator.
  
  This density estimator can handle univariate as well as multivariate data,
  including mixed continuous / ordered discrete / unordered discrete data.
  It also provides cross-validated bandwidth selection methods (least
  squares, maximum likelihood).
  
  Parameters
  ----------
  data : list of ndarrays or 2-D ndarray
      The training data for the Kernel Density Estimation, used to determine
      the bandwidth(s).  If a 2-D array, should be of shape
      (num_observations, num_variables).  If a list, each list element is a
      separate observation.
  var_type : str
      The type of the variables:
  
          - c : continuous
          - u : unordered (discrete)
          - o : ordered (discrete)
  
      The string should contain a type specifier for each variable, so for
      example ``var_type='ccuo'``.
  bw : array_like or str, optional
      If an array, it is a fixed user-specified bandwidth.  If a string,
      should be one of:
  
          - normal_reference: normal reference rule of thumb (default)
          - cv_ml: cross validation maximum likelihood
          - cv_ls: cross validation least squares
  
  defaults : EstimatorSettings instance, optional
      The default values for (efficient) bandwidth estimation.
  
  Attributes
  ----------
  bw : array_like
      The bandwidth parameters.
  
  See Also
  --------
  KDEMultivariateConditional
  
  Examples
  --------
  >>> import statsmodels.api as sm
  >>> nobs = 300
  >>> np.random.seed(1234)  # Seed random generator
  >>> c1 = np.random.normal(size=(nobs,1))
  >>> c2 = np.random.normal(2, 1, size=(nobs,1))
  
  Estimate a bivariate distribution and display the bandwidth found:
  
  >>> dens_u = sm.nonparametric.KDEMultivariate(data=[c1,c2],
  ...     var_type='cc', bw='normal_reference')
  >>> dens_u.bw
  array([ 0.39967419,  0.38423292])
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docstr: Evaluate the cumulative distribution function.
  
  Parameters
  ----------
  data_predict : array_like, optional
      Points to evaluate at.  If unspecified, the training data is used.
  
  Returns
  -------
  cdf_est : array_like
      The estimate of the cdf.
  
  Notes
  -----
  See https://en.wikipedia.org/wiki/Cumulative_distribution_function
  For more details on the estimation see Ref. [5] in module docstring.
  
  The multivariate CDF for mixed data (continuous and ordered/unordered
  discrete) is estimated by:
  
  .. math::
  
      F(x^{c},x^{d})=n^{-1}\sum_{i=1}^{n}\left[G(\frac{x^{c}-X_{i}}{h})\sum_{u\leq x^{d}}L(X_{i}^{d},x_{i}^{d}, \lambda)\right]
  
  where G() is the product kernel CDF estimator for the continuous
  and L() for the discrete variables.
  
  Used bandwidth is ``self.bw``.
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code: def cdf(self, data_predict=None):
      r"""
      Evaluate the cumulative distribution function.
  
      Parameters
      ----------
      data_predict : array_like, optional
          Points to evaluate at.  If unspecified, the training data is used.
  
      Returns
      -------
      cdf_est : array_like
          The estimate of the cdf.
  
      Notes
      -----
      See https://en.wikipedia.org/wiki/Cumulative_distribution_function
      For more details on the estimation see Ref. [5] in module docstring.
  
      The multivariate CDF for mixed data (continuous and ordered/unordered
      discrete) is estimated by:
  
      .. math::
  
          F(x^{c},x^{d})=n^{-1}\sum_{i=1}^{n}\left[G(\frac{x^{c}-X_{i}}{h})\sum_{u\leq x^{d}}L(X_{i}^{d},x_{i}^{d}, \lambda)\right]
  
      where G() is the product kernel CDF estimator for the continuous
      and L() for the discrete variables.
  
      Used bandwidth is ``self.bw``.
      """
      if data_predict is None:
          data_predict = self.data
      else:
          data_predict = _adjust_shape(data_predict, self.k_vars)
  
      cdf_est = []
      for i in range(np.shape(data_predict)[0]):
          cdf_est.append(
              gpke(
                  self.bw,
                  data=self.data,
                  data_predict=data_predict[i, :],
                  var_type=self.var_type,
                  ckertype="gaussian_cdf",
                  ukertype="aitchisonaitken_cdf",
                  okertype="wangryzin_cdf",
              )
              / self.nobs
          )
  
      cdf_est = np.squeeze(cdf_est)
      return cdf_est
  
imports: import numpy
  from .None import kernels
  from ._kernel_base import GenericKDE, EstimatorSettings, gpke, LeaveOneOut, _adjust_shape
label_desc: Use image node_id 5 for calling the KDEMultivariate obj's underlying member method code with example usage: obj.cdf(data_predict) and returns: cdf_est