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})