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

  EXPECT_EQ(statistics.value().histogram_statistics().bin_width(), 2.f);
  // Trailing zeros should be removed.
  EXPECT_THAT(statistics.value().histogram_statistics().hist_freq(),
              ElementsAre(1, 0, 3, 5, 7, 6, 5));
}

TEST(HistogramStatisticsCollectorTest, AggregateSameBatchSize) {
  CalibrationOptions calib_opts;
  calib_opts.set_calibration_method(

    // 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;

    hist_stats = statistics.histogram_statistics
    self._bin_width = hist_stats.bin_width
    self._lower_bound = hist_stats.lower_bound
    self._hist_freq = np.array(hist_stats.hist_freq)
    self._num_bins = len(self._hist_freq)
    self._num_bits = 8
    # i-th bin has a range [bins[i], bins[i + 1]).
    # bins[i] = lower_bound + i * bin_width
    # bins[i + 1] = lower_bound + (i + 1) * bin_width

  ASSERT_TRUE(stats.has_histogram_statistics());
  EXPECT_FLOAT_EQ(stats.histogram_statistics().bin_width(), 0.5f);
  EXPECT_FLOAT_EQ(stats.histogram_statistics().lower_bound(), 1.f);
  EXPECT_THAT(stats.histogram_statistics().hist_freq(),
              ElementsAre(1, 4, 6, 7, 3, 2, 1));
}

TEST_F(CalibrationStatisticsSaverTest, MultipleStats) {
  std::vector<std::string> ids{"1", "2"};
  std::vector<int32_t> calibration_methods{

  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_;
};