code: def test_loguniform():
      min_included = 0.001
      max_included = 10
      hd = LogUniform(min_included, max_included)
  
      samples = hd_rvs_many(hd)
  
      samples_mean = np.abs(np.mean(samples))
      assert (
          samples_mean < 1.15
      )  # if it was just uniform, this assert would break.
      assert min(samples) >= 0.001
      assert max(samples) <= 10.0
      assert hd.pdf(0.0001) == 0.0
      assert abs(hd.pdf(2) - 0.054286810237906484) < 1e-6
      assert hd.pdf(10.1) == 0.0
      assert hd.cdf(0.0001) == 0.0
      assert (
          abs(
              hd.cdf(2)
              - (math.log2(2) - math.log2(0.001))
              / (math.log2(10) - math.log2(0.001))
          )
          < 1e-6
      )
      assert hd.cdf(10.1) == 1.0
  
      assert hd.min() == min_included
      assert hd.max() == max_included
      assert (
          abs(
              hd.mean()
              - (max_included - min_included)
              / (
                  math.log(2)
                  * (math.log2(max_included) - math.log2(min_included))
              )
          )
          < 1e-6
      )
      esperance_squared = (max_included**2 - min_included**2) / (
          2
          * math.log(2)
          * (math.log2(max_included) - math.log2(min_included))
      )
      assert abs(hd.var() - (esperance_squared - hd.mean() ** 2)) < 1e-6
      # Verify that hd mean and variance also correspond to mean and variance of sampling.
      assert abs(hd.mean() - np.mean(samples)) < 5e-2
      assert abs(hd.var() - np.var(samples)) < 2.5e-1
  
imports: import random
  from collections import Counter
  import numpy
  import pytest
  from neuraxle.hyperparams.distributions import *
label_desc: Use image node_id 9 for calling a global function with example usage: test_loguniform() without return types