code: def pdf_internal(x, df, loc=0.0, scale=1.0, gamma = 1.0):
          
          result = np.zeros(x.shape[0])
          result[x<0] = 2.0/(gamma + 1.0/gamma)*stats.t.pdf(x=gamma*x[(x-loc) < 0], loc=loc[(x-loc) < 0]*gamma,df=df, scale=scale)
          result[x>=0] = 2.0/(gamma + 1.0/gamma)*stats.t.pdf(x=x[(x-loc) >= 0]/gamma, loc=loc[(x-loc) >= 0]/gamma,df=df, scale=scale)
          return result
docs: Raw PDF function for the Skew t distribution