def test_second_moment_positive_left_of_mean(self):
mu = 4
sigma = 2
a = 0
b = 1
actual = Moments(mu=mu, sigma=sigma, a=a, b=b).second_moment
assert actual > 0
def test_second_moment_positive(self):
mu = -4
sigma = 2
a = -np.inf
b = np.inf
actual = Moments(mu=mu, sigma=sigma, a=a, b=b).second_moment
assert actual > 0
def test_second_moment_positive_truncated(self):
mu = 4
sigma = 2
a = -2
b = 5
actual = Moments(mu=mu, sigma=sigma, a=a, b=b).second_moment
assert actual > 0
def test_second_moment_negative_mean(self):
mu = -4
sigma = 2
a = -np.inf
b = np.inf
actual = Moments(mu=mu, sigma=sigma, a=a, b=b).second_moment
expected = mu**2 + sigma**2
assert actual == expected
def test_first_moment_negative_mean(self):
first = Moments(-5, 3, -np.inf, np.inf).first_moment
assert first == -5
def test_first_moment_positive_mean(self):
first = Moments(5, 3, -np.inf, np.inf).first_moment
assert first == 5
def test_second_moment_standard_normal(self):
second = Moments(0, 1, -np.inf, np.inf).second_moment
assert second == 1.0
def test_first_moment_standard_normal(self):
first = Moments(0, 1, -np.inf, np.inf).first_moment
assert first == 0