class_docstr: Student's t-distribution (sktime native).
  
  Parameters
  ----------
  mean : float or array of float (1D or 2D)
      mean of the t-distribution distribution
  sd : float or array of float (1D or 2D), must be positive
      standard deviation of the t-distribution distribution
  df : float or array of float (1D or 2D), must be positive
      Degrees of freedom of the t-distribution
  index : pd.Index, optional, default = RangeIndex
  columns : pd.Index, optional, default = RangeIndex
  
  Example
  -------
  >>> from sktime.proba.t import TDistribution
  
  >>> n = TDistribution(mu=[[0, 1], [2, 3], [4, 5]], sigma=1, df=10)
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docstr: Logarithmic probability density function.
docstr_tok: ["Logarithmic","probability","density","function","."]
code: def log_pdf(self, x):
      """Logarithmic probability density function."""
      d = self.loc[x.index, x.columns]
      lpdf_arr = loggamma((d._df + 1) / 2)
      lpdf_arr = lpdf_arr - 0.5 * np.log(d._df * np.pi)
      lpdf_arr = lpdf_arr - loggamma(d._df / 2)
      lpdf_arr = lpdf_arr - ((d._df + 1) / 2) * np.log(
          1 + x**2 / d._df
      )
      return pd.DataFrame(lpdf_arr, index=x.index, columns=x.columns)
  
file_path: sktime/sktime/proba/t.py
imports: import numpy
  import pandas
  from scipy.special import betaincinv, gamma, hyp2f1, loggamma
  from sktime.proba.base import BaseDistribution
label_desc: Use image node_id 5 for calling the TDistribution obj's underlying member method code with example usage: obj.log_pdf(x) and returns: pd