code: def tstd_pdf(x, df):
      """pdf for standardized (not standard) t distribution, variance is one"""
  
      r = np.array(df * 1.0)
      Px = np.exp(
          special.gammaln((r + 1) / 2.0) - special.gammaln(r / 2.0)
      ) / np.sqrt((r - 2) * np.pi)
      Px /= (1 + (x**2) / (r - 2)) ** ((r + 1) / 2.0)
      return Px
  
file_path: statsmodels/statsmodels/sandbox/regression/tools.py
imports: import numpy
  from scipy import special
  from scipy.special import gammaln
label_desc: Use image node_id 7 for calling a global function with example usage: tstd_pdf(x, df) and returns: Px