code: def test_boltzmann_upper_bound():
      k = np.arange(-3, 5)
  
      N = 1
      p = boltzmann.pmf(k, 0.123, N)
      expected = k == 0
      assert_equal(p, expected)
  
      lam = np.log(2)
      N = 3
      p = boltzmann.pmf(k, lam, N)
      expected = [0, 0, 0, 4 / 7, 2 / 7, 1 / 7, 0, 0]
      assert_allclose(p, expected, rtol=1e-13)
  
      c = boltzmann.cdf(k, lam, N)
      expected = [0, 0, 0, 4 / 7, 6 / 7, 1, 1, 1]
      assert_allclose(c, expected, rtol=1e-13)
  
imports: from __future__ import division, print_function, absolute_import
  from scipy.stats import hypergeom, bernoulli, boltzmann
  import numpy
  from numpy.testing import assert_almost_equal, assert_equal, assert_allclose
label_desc: Use image node_id 2 for calling a global function with example usage: test_boltzmann_upper_bound() without return types