class_docstr: Student t Distribution
  ----
  This class contains methods relating to the Student t distribution for time series.
class_docstr_tok: ["Student","t","Distribution","--","--","This","class","contains","methods","relating","to","the","Student","t","distribution","for","time","series","."]
docstr: Creates approximating Gaussian state space model for t measurement density
  
  Parameters
  ----------
  beta : np.array
      Contains untransformed starting values for latent variables
  
  T, Z, R, Q : np.array
      State space matrices used in KFS algorithm
  
  h_approx : float
      The variance of the measurement density
  
  data: np.array
      The univariate time series data
  
  X: np.array
      The regressors
  
  state_no : int
      Number of states
  
  Returns
  ----------
  H : np.array
      Approximating measurement variance matrix
  
  mu : np.array
      Approximating measurement constants
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code: def approximating_model_reg(
      self, beta, T, Z, R, Q, h_approx, data, X, state_no
  ):
      """Creates approximating Gaussian state space model for t measurement density
  
      Parameters
      ----------
      beta : np.array
          Contains untransformed starting values for latent variables
  
      T, Z, R, Q : np.array
          State space matrices used in KFS algorithm
  
      h_approx : float
          The variance of the measurement density
  
      data: np.array
          The univariate time series data
  
      X: np.array
          The regressors
  
      state_no : int
          Number of states
  
      Returns
      ----------
      H : np.array
          Approximating measurement variance matrix
  
      mu : np.array
          Approximating measurement constants
      """
  
      H = np.ones(data.shape[0]) * h_approx
      mu = np.zeros(data.shape[0])
  
      return H, mu
  
imports: import numpy
  import scipy.stats
  import scipy.special
  from .family import Family
  from .flat import Flat
  from .normal import Normal
  from .gas_recursions import gas_recursion_t_orderone, gas_recursion_t_ordertwo
  from .gas_recursions import gasx_recursion_t_orderone, gasx_recursion_t_ordertwo
  from .gas_recursions import gas_llev_recursion_t_orderone, gas_llev_recursion_t_ordertwo
  from .gas_recursions import gas_llt_recursion_t_orderone, gas_llt_recursion_t_ordertwo
  from .gas_recursions import gas_reg_recursion_t_orderone, gas_reg_recursion_t_ordertwo
label_desc: Use image node_id 3 for calling the t obj's underlying member method code with example usage: obj.approximating_model_reg(beta, T, Z, R, Q, h_approx, data, X, state_no) and returns: H,  mu