code: def _checkKLApprox(self, df, loc, sigma, samples):
      n = samples.size
      np.random.seed(137)
      sample_scipy = (
          np.abs(sp_stats.t.rvs(df, loc=0.0, scale=sigma, size=n)) + loc
      )
      covg = 0.99
      _, right = sp_stats.t.interval(
          0.5 * (1 + covg), df, loc=loc, scale=sigma
      )
      r = (loc, right)
      bins = 100
      hist, _ = np.histogram(samples, bins=bins, range=r)
      hist_scipy, _ = np.histogram(sample_scipy, bins=bins, range=r)
      self.assertGreater(hist.sum(), n * (covg - 0.01))
      self.assertGreater(hist_scipy.sum(), n * (covg - 0.01))
      hist_min1 = hist + 1.0  # put at least one item in each bucket
      hist_norm = hist_min1 / hist_min1.sum()
      hist_scipy_min1 = (
          hist_scipy + 1.0
      )  # put at least one item in each bucket
      hist_scipy_norm = hist_scipy_min1 / hist_scipy_min1.sum()
      kl_appx = np.sum(
          np.log(hist_scipy_norm / hist_norm) * hist_scipy_norm
      )
      self.assertLess(kl_appx, 1)
  
imports: import math
  import numpy
  from scipy import stats
  from scipy.special import gamma
  import tensorflow.compat.v2
  from tensorflow_probability.python.distributions import half_student_t
  from tensorflow_probability.python.distributions.internal import statistical_testing
  from tensorflow_probability.python.internal import assert_util
  from tensorflow_probability.python.internal import test_util
  from tensorflow_probability.python.math import gradient
label_desc: Use image node_id 9 for calling the HalfStudentTTest obj's underlying member method code with example usage: obj._checkKLApprox(df, loc, sigma, samples) without return types