text: #ifndef STAN_MATH_PRIM_SCAL_PROB_BINOMIAL_LOGIT_LPMF_HPP
  #define STAN_MATH_PRIM_SCAL_PROB_BINOMIAL_LOGIT_LPMF_HPP
  
  #include <stan/math/prim/scal/meta/is_constant_struct.hpp>
  #include <stan/math/prim/scal/meta/partials_return_type.hpp>
  #include <stan/math/prim/scal/meta/operands_and_partials.hpp>
  #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
  #include <stan/math/prim/scal/err/check_bounded.hpp>
  #include <stan/math/prim/scal/err/check_finite.hpp>
  #include <stan/math/prim/scal/err/check_greater_or_equal.hpp>
  #include <stan/math/prim/scal/err/check_less_or_equal.hpp>
  #include <stan/math/prim/scal/err/check_nonnegative.hpp>
  #include <stan/math/prim/scal/fun/size_zero.hpp>
  #include <stan/math/prim/scal/fun/constants.hpp>
  #include <stan/math/prim/scal/fun/inv_logit.hpp>
  #include <stan/math/prim/scal/fun/log1m.hpp>
  #include <stan/math/prim/scal/fun/log_inv_logit.hpp>
  #include <stan/math/prim/scal/fun/multiply_log.hpp>
  #include <stan/math/prim/scal/fun/value_of.hpp>
  #include <stan/math/prim/scal/fun/binomial_coefficient_log.hpp>
  #include <stan/math/prim/scal/fun/lbeta.hpp>
  #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
  #include <stan/math/prim/scal/meta/include_summand.hpp>
  #include <stan/math/prim/scal/meta/scalar_seq_view.hpp>
  #include <stan/math/prim/scal/fun/inc_beta.hpp>
  #include <boost/random/binomial_distribution.hpp>
  #include <boost/random/variate_generator.hpp>
  
  namespace stan {
  namespace math {
  
  /**
   * Binomial log PMF in logit parametrization. Binomial(n|n, inv_logit(alpha))
   *
   * If given vectors of matching lengths, returns
   * the log sum of probabilities.
   *
   * @param n successes variable
   * @param N population size parameter
   * @param alpha logit transformed probability parameter
   *
   * @return log probability or log sum of probabilities
   *
   * @throw std::domain_error if N is negative or probability parameter is invalid
   * @throw std::invalid_argument if vector sizes do not match
   */
  template <bool propto, typename T_n, typename T_N, typename T_prob>
  typename return_type<T_prob>::type binomial_logit_lpmf(const T_n& n,
                                                         const T_N& N,
                                                         const T_prob& alpha) {
    typedef typename stan::partials_return_type<T_n, T_N, T_prob>::type
        T_partials_return;
  
    static const char* function = "binomial_logit_lpmf";
  
    if (size_zero(n, N, alpha))
      return 0.0;
  
    T_partials_return logp = 0;
    check_bounded(function, "Successes variable", n, 0, N);
    check_nonnegative(function, "Population size parameter", N);
    check_finite(function, "Probability parameter", alpha);
    check_consistent_sizes(function, "Successes variable", n,
                           "Population size parameter", N,
                           "Probability parameter", alpha);
  
    if (!include_summand<propto, T_prob>::value)
      return 0.0;
  
    scalar_seq_view<T_n> n_vec(n);
    scalar_seq_view<T_N> N_vec(N);
    scalar_seq_view<T_prob> alpha_vec(alpha);
    size_t size = max_size(n, N, alpha);
  
    operands_and_partials<T_prob> ops_partials(alpha);
  
    if (include_summand<propto>::value) {
      for (size_t i = 0; i < size; ++i)
        logp += binomial_coefficient_log(N_vec[i], n_vec[i]);
    }
  
    VectorBuilder<true, T_partials_return, T_prob> log_inv_logit_alpha(
        length(alpha));
    for (size_t i = 0; i < length(alpha); ++i)
      log_inv_logit_alpha[i] = log_inv_logit(value_of(alpha_vec[i]));
  
    VectorBuilder<true, T_partials_return, T_prob> log_inv_logit_neg_alpha(
        length(alpha));
    for (size_t i = 0; i < length(alpha); ++i)
      log_inv_logit_neg_alpha[i] = log_inv_logit(-value_of(alpha_vec[i]));
  
    for (size_t i = 0; i < size; ++i)
      logp += n_vec[i] * log_inv_logit_alpha[i]
              + (N_vec[i] - n_vec[i]) * log_inv_logit_neg_alpha[i];
  
    if (length(alpha) == 1) {
      T_partials_return temp1 = 0;
      T_partials_return temp2 = 0;
      for (size_t i = 0; i < size; ++i) {
        temp1 += n_vec[i];
        temp2 += N_vec[i] - n_vec[i];
      }
      if (!is_constant_struct<T_prob>::value) {
        ops_partials.edge1_.partials_[0]
            += temp1 * inv_logit(-value_of(alpha_vec[0]))
               - temp2 * inv_logit(value_of(alpha_vec[0]));
      }
    } else {
      if (!is_constant_struct<T_prob>::value) {
        for (size_t i = 0; i < size; ++i)
          ops_partials.edge1_.partials_[i]
              += n_vec[i] * inv_logit(-value_of(alpha_vec[i]))
                 - (N_vec[i] - n_vec[i]) * inv_logit(value_of(alpha_vec[i]));
      }
    }
  
    return ops_partials.build(logp);
  }
  
  template <typename T_n, typename T_N, typename T_prob>
  inline typename return_type<T_prob>::type binomial_logit_lpmf(
      const T_n& n, const T_N& N, const T_prob& alpha) {
    return binomial_logit_lpmf<false>(n, N, alpha);
  }
  
  }  // namespace math
  }  // namespace stan
  #endif
  