def test_cdf():
D = Die('D', 6)
o = Integer(1)
assert cdf(D) == sympify({
1: o / 6,
2: o / 3,
3: o / 2,
4: 2 * o / 3,
5: 5 * o / 6,
6: o
})
def test_cdf():
X = Normal('x', 0, 1)
d = cdf(X)
assert P(X < 1) == d(1)
assert d(0) == S.Half
d = cdf(X, X > 0) # given X>0
assert d(0) == 0
Y = Exponential('y', 10)
d = cdf(Y)
assert d(-5) == 0
assert P(Y > 3) == 1 - d(3)
pytest.raises(ValueError, lambda: cdf(X + Y))
Z = Exponential('z', 1)
f = cdf(Z)
z = Symbol('z')
assert f(z) == Piecewise((1 - exp(-z), z >= 0), (0, True))
def test_cdf():
X = Normal('x', 0, 1)
d = cdf(X)
assert P(X < 1) == d(1)
assert d(0) == Rational(1, 2)
d = cdf(X, X > 0) # given X>0
assert d(0) == 0
Y = Exponential('y', 10)
d = cdf(Y)
assert d(-5) == 0
assert P(Y > 3) == 1 - d(3)
pytest.raises(ValueError, lambda: cdf(X + Y))
Z = Exponential('z', 1)
f = cdf(Z)
z = Symbol('z')
assert f(z) == Piecewise((1 - exp(-z), z >= 0), (0, True))
U = Uniform('x', 3, 5)
u = cdf(U)
assert u(z) == z/2 - Rational(3, 2)
def test_gamma():
k = Symbol('k', positive=True)
theta = Symbol('theta', positive=True)
X = Gamma('x', k, theta)
assert density(X)(x) == x**(k - 1)*theta**(-k)*exp(-x/theta)/gamma(k)
assert cdf(X, meijerg=True)(z) == Piecewise(
(-k*lowergamma(k, 0)/gamma(k + 1) +
k*lowergamma(k, z/theta)/gamma(k + 1), z >= 0),
(0, True))
# assert simplify(variance(X)) == k*theta**2 # handled numerically below
assert E(X) == moment(X, 1)
k, theta = symbols('k theta', real=True, positive=True)
X = Gamma('x', k, theta)
assert simplify(E(X)) == k*theta
# can't get things to simplify on this one so we use subs
assert variance(X).subs({k: 5}) == (k*theta**2).subs({k: 5})
def test_gamma():
k = Symbol("k", positive=True)
theta = Symbol("theta", positive=True)
X = Gamma('x', k, theta)
assert density(X)(x) == x**(k - 1)*theta**(-k)*exp(-x/theta)/gamma(k)
assert cdf(X, meijerg=True)(z) == Piecewise(
(-k*lowergamma(k, 0)/gamma(k + 1) +
k*lowergamma(k, z/theta)/gamma(k + 1), z >= 0),
(0, True))
# assert simplify(variance(X)) == k*theta**2 # handled numerically below
assert E(X) == moment(X, 1)
k, theta = symbols('k theta', real=True, positive=True)
X = Gamma('x', k, theta)
assert simplify(E(X)) == k*theta
# can't get things to simplify on this one so we use subs
assert variance(X).subs({k: 5}) == (k*theta**2).subs({k: 5})
def test_cdf():
D = Die('D', 6)
o = Integer(1)
assert cdf(
D) == sympify({1: o/6, 2: o/3, 3: o/2, 4: 2*o/3, 5: 5*o/6, 6: o})
