hist_freq = np.zeros(501, dtype=np.int32)

    # Advanced calibration methods that use histograms detect outliers, so they
    # don't use the outliers as min/max values.
    hist_freq[0] = 1
    hist_freq[-1] = 1

    # The majority of the data exists around the center.
    hist_freq[250] = 1000
    for i in range(1, 201):
      hist_freq[250 - i] = 1000 - i

    // lower_bound and bin_width can be used to restore the histogram.
    float lower_bound = 2;

    // hist_freq[i] saves frequency of range [bins[i], bins[i + 1]).
    // bins[i]     = lower_bound + bin_width * i
    // bins[i + 1] = lower_bound + bin_width * (i + 1)
    repeated float hist_freq = 3;
  }

  MinMaxStatistics min_max_statistics = 1;
  AverageMinMaxStatistics average_min_max_statistics = 2;

  if (lower_idx < 0) {
    hist_freq_.insert(hist_freq_.begin(), -lower_idx, 0);
    lower_bound_ -= bin_width_ * (-lower_idx);
    lower_idx = 0;
  }

  int32_t upper_idx = CalculateBinIndex(upper_bound, lower_bound_, bin_width_);
  // If upper_idx >= hist_freq_.size(), then expand the histogram to the right.
  if (upper_idx >= hist_freq_.size()) {
    hist_freq_.resize(upper_idx + 1, 0);
  }

                                                      float upper_bound);

  // hist_freq_[i] saves frequency of range [bins[i], bins[i + 1]).
  // bins[i]     = lower_bound_ + bin_width_ * i
  // bins[i + 1] = lower_bound_ + bin_width_ * (i + 1)
  std::deque<float> hist_freq_;

  // Width of bin
  float bin_width_;

  // The first bin's left value. [left, right)
  float lower_bound_;
};