def test_pmf_no_inflation(self):
dist1 = KInflatedGammaPoissonDistribution(1.0, 1.0, [])
self.assertAlmostEqual(dist1.pmf(1), gamma_poisson_pmf(0, 1.0, 1.0))
self.assertAlmostEqual(dist1.pmf(2), gamma_poisson_pmf(1, 1.0, 1.0))
dist2 = KInflatedGammaPoissonDistribution(3.0, 1.0, [])
self.assertAlmostEqual(dist2.pmf(2), gamma_poisson_pmf(1, 3.0, 1.0))
dist3 = KInflatedGammaPoissonDistribution(1.0, 4.0, [])
self.assertAlmostEqual(dist3.pmf(2), gamma_poisson_pmf(1, 1.0, 4.0))
def test_knreach_no_inflation(self):
dist = KInflatedGammaPoissonDistribution(1.0, 1.0, [])
self.assertAlmostEqual(dist.knreach(1, 1, 0.5), 0.25)
self.assertAlmostEqual(dist.knreach(2, 1, 0.5), 0)
self.assertAlmostEqual(dist.knreach(1, 1, 0.5), 1.0 / 4.0)
self.assertAlmostEqual(dist.knreach(1, np.array([1]), 0.5)[0], 1 / 4)
self.assertAlmostEqual(
dist.knreach(1, np.array([1, 2]), 0.5)[0], 1 / 4)
self.assertAlmostEqual(
dist.knreach(1, np.array([1, 2]), 0.5)[1], 1 / 8)
self.assertAlmostEqual(dist.knreach(1, 3, 1 / 3),
3 * (1 / 3) * (2 / 3)**2 * (1 / 8))
def test_kreach_no_inflation(self):
dist = KInflatedGammaPoissonDistribution(1.0, 1.0, [])
self.assertAlmostEqual(dist.kreach([0], 0.5)[0], 1 / 3)
self.assertAlmostEqual(dist.kreach([0], 1 / 3)[0], 1 / 2)
self.assertAlmostEqual(dist.kreach([1], 1 / 3)[0], 3 / 8)
self.assertAlmostEqual(dist.kreach([0, 1, 2], 1 / 3)[0], 1 / 2)
self.assertAlmostEqual(dist.kreach([0, 1, 2], 1 / 3)[1], 3 / 8)
self.assertAlmostEqual(dist.kreach([0, 1, 2], 1 / 3)[2], 3 / 32)
def test_pmf_with_partial_inflation(self):
dist1 = KInflatedGammaPoissonDistribution(1.0, 1.0, [0.5])
self.assertAlmostEqual(dist1.pmf(1), 0.5)
scale_factor = 0.5 / (1.0 - gamma_poisson_pmf(0, 1.0, 1.0))
expected = scale_factor * gamma_poisson_pmf(1, 1.0, 1.0)
self.assertAlmostEqual(dist1.pmf(2), expected)
dist2 = KInflatedGammaPoissonDistribution(3.0, 1.0, [0.5])
scale_factor = 0.5 / (1.0 - gamma_poisson_pmf(0, 3.0, 1.0))
expected = scale_factor * gamma_poisson_pmf(1, 3.0, 1.0)
self.assertAlmostEqual(dist2.pmf(2), expected)
def test_by_impressions(self, mock_fit_point):
mock_fit_point.return_value = (
10000,
KInflatedGammaPoissonDistribution(5.0, 2.0, []),
)
# Imax = 25000, N = 10000, alpha = 5, beta = 2
h_training = [7412, 4233, 2014, 842, 320, 112, 37, 11, 2]
rp = ReachPoint([15000], h_training, [200.0])
kgpm = KInflatedGammaPoissonModel([rp])
kgpm._fit()
rp = kgpm.by_impressions([10000], max_frequency=5)
h_expected = np.array([6056, 2629, 925, 283, 78])
h_actual = np.array([int(rp.reach(i)) for i in range(1, 6)])
total_error = np.sum((h_expected - h_actual)**2 / h_expected)
self.assertAlmostEqual(rp.spends[0], 133.0, delta=1)
for i in range(len(h_actual)):
self.assertTrue(
(h_actual[i] - h_expected[i])**2 / h_actual[i] < 0.1,
f"Discrepancy found at position {i}. "
f"Got {h_actual[i]} Expected {h_expected[i]}",
)
def test_pmf_with_full_inflation(self):
dist = KInflatedGammaPoissonDistribution(1.0, 1.0, [0.75, 0.25])
self.assertAlmostEqual(dist.pmf(1), 0.75)
self.assertAlmostEqual(dist.pmf(2), 0.25)
self.assertAlmostEqual(dist.pmf(3), 0.0)
def test_expected_value(self):
dist1 = KInflatedGammaPoissonDistribution(1.0, 1.0, [])
self.assertAlmostEqual(dist1.expected_value(), 2.0)
dist2 = KInflatedGammaPoissonDistribution(2.0, 1.0, [])
self.assertAlmostEqual(dist2.expected_value(), 3.0)
dist3 = KInflatedGammaPoissonDistribution(1.0, 2.0, [])
self.assertAlmostEqual(dist3.expected_value(), 3.0)
dist4 = KInflatedGammaPoissonDistribution(1.0, 2.0, [1.0])
self.assertAlmostEqual(dist4.expected_value(), 1.0)
dist5 = KInflatedGammaPoissonDistribution(1.0, 2.0, [0.5, 0.5])
self.assertAlmostEqual(dist5.expected_value(), 1.5)