code: def conditional_probability_alive(self, frequency, recency, T):
          
          x, t_x = frequency, recency
          r, alpha, s, beta = self._unload_params("r", "alpha", "s", "beta")
          A_0 = self._log_A_0([r, alpha, s, beta], x, t_x, T)
          return 1.0 / (1.0 + exp(log(s) - log(r + s + x) + (r + x) * log(alpha + T) + s * log(beta + T) + A_0))
docs: Conditional probability alive.
  
          Compute the probability that a customer with history
          (frequency, recency, T) is currently alive.
          From paper:
          http://brucehardie.com/notes/009/pareto_nbd_derivations_2005-11-05.pdf
  
          Parameters
          ----------
          frequency: float
              historical frequency of customer.
          recency: float
              historical recency of customer.
          T: float
              age of the customer.
  
          Returns
          -------
          float
              value representing a probability