def test_mean_variance(self):
g = Gamma.from_mean_variance(2.0, 3.0)
self.assertEqual(g.mean(), 2.0)
self.assertEqual(g.variance(), 3.0)
g = Gamma.from_mean_variance(2.0123, 3.01283)
self.assertEqual(g.mean(), 2.0123)
self.assertEqual(g.variance(), 3.01283)
def test_inverse_cdf(self):
g = Gamma.from_mean_variance(2.34, 4)
self.assertAlmostEqual(3.9, g.inverse_cdf(g.cdf(3.9)))
self.assertAlmostEqual(1.92, g.inverse_cdf(g.cdf(1.92)))
g = Gamma.from_mean_variance(10.34, 2)
self.assertAlmostEqual(3.9, g.inverse_cdf(g.cdf(3.9)))
self.assertAlmostEqual(10.92, g.inverse_cdf(g.cdf(10.92)))
g = Gamma.from_mean_variance(10.34, 2)
self.assertAlmostEqual(0.975, g.cdf(g.inverse_cdf(0.975)))
self.assertAlmostEqual(0.025, g.cdf(g.inverse_cdf(0.025)))
g = Gamma.from_mean_variance(1.34, 4)
self.assertAlmostEqual(0.975, g.cdf(g.inverse_cdf(0.975)))
self.assertAlmostEqual(0.025, g.cdf(g.inverse_cdf(0.025)))
def test_sample(self):
m = 10.0
v = 2.0
g = Gamma.from_mean_variance(m, v)
# print(g.alpha, g.beta)
S = 1000
total = 0.0
for s in range(S):
total += g.sample()
mean = total / S
# The estimated mean will differ from true mean by a small amount
error = 4.0 * sqrt(g.variance() / S)
# print(mean, m, error)
self.assertTrue(abs(mean - m) < error)
def test_cdf(self):
m = 3.0
v = 2.0
g = Gamma.from_mean_variance(m, v)
# Numerical integration
S = 1000
M = 10.0
total_p = 0.0
epsilon = 1e-4
last = 0.0
for s in range(S):
x = s * M / S
p = g.pdf(x) * M / S
total_p += (last - p) / 2.0
last = p
# print(x, total_p, g.cdf(x))
self.assertTrue((total_p - g.cdf(x)) < epsilon)
def test_pdf(self):
m = 3.0
v = 2.0
g = Gamma.from_mean_variance(m, v)
upper = 30.0
norm = integrate(g.pdf, 0, upper)
self.assertAlmostEqual(norm, 1.0)
def fx(x):
return x * g.pdf(x)
mean = integrate(fx, 0, upper)
self.assertAlmostEqual(mean, m)
def fx2(x):
return x * x * g.pdf(x)
x2 = integrate(fx2, 0, upper)
var = x2 - mean**2
self.assertAlmostEqual(var, v)