class_docstr: Class for Multivariate Normal Distribution
  
  uses Cholesky decomposition of covariance matrix for the transformation
  of the data
class_docstr_tok: ["Class","for","Multivariate","Normal","Distribution","uses","Cholesky","decomposition","of","covariance","matrix","for","the","transformation","of","the","data"]
docstr: return distribution of an affine transform
  
  for full rank scale_matrix only
  
  Parameters
  ----------
  shift : array_like
      shift of mean
  scale_matrix : array_like
      linear transformation matrix
  
  Returns
  -------
  mvt : instance of MVNormal
      instance of multivariate normal distribution given by affine
      transformation
  
  Notes
  -----
  the affine transformation is defined by
  y = a + B x
  
  where a is shift,
  B is a scale matrix for the linear transformation
  
  Notes
  -----
  This should also work to select marginal distributions, but not
  tested for this case yet.
  
  currently only tested because it's called by standardized
code: def affine_transformed(self, shift, scale_matrix):
      """return distribution of an affine transform
  
      for full rank scale_matrix only
  
      Parameters
      ----------
      shift : array_like
          shift of mean
      scale_matrix : array_like
          linear transformation matrix
  
      Returns
      -------
      mvt : instance of MVNormal
          instance of multivariate normal distribution given by affine
          transformation
  
      Notes
      -----
      the affine transformation is defined by
      y = a + B x
  
      where a is shift,
      B is a scale matrix for the linear transformation
  
      Notes
      -----
      This should also work to select marginal distributions, but not
      tested for this case yet.
  
      currently only tested because it's called by standardized
  
      """
      B = scale_matrix  # tmp variable
      mean_new = np.dot(B, self.mean) + shift
      sigma_new = np.dot(np.dot(B, self.sigma), B.T)
      return MVNormal(mean_new, sigma_new)
  
imports: import numpy
  from scipy import special
  from statsmodels.sandbox.distributions.multivariate import mvstdtprob
  from .extras import mvnormcdf
label_desc: Use image node_id 5 for calling the MVNormal obj's underlying member method code with example usage: obj.affine_transformed(shift, scale_matrix) and returns: MVNormal