  /* compute the cauchit link 
   * Args: 
   *   p: a scalar in (0, 1)
   * Returns: 
   *   a scalar in (-Inf, Inf)
   */ 
   real cauchit(real p) { 
     return tan(pi() * (p - 0.5)); 
   }
  /* compute the inverse of the cauchit link 
   * Args: 
   *   y: a scalar in (-Inf, Inf)
   * Returns: 
   *   a scalar in (0, 1)
   */ 
   real inv_cauchit(real y) { 
     return cauchy_cdf(y, 0, 1); 
   }
