def test_GeometricDistribution(): p = S.One / 5 d = GeometricDistribution(p) assert d.expectation(x, x) == 1/p assert d.expectation(x**2, x) - d.expectation(x, x)**2 == (1-p)/p**2 assert abs(d.cdf(20000).evalf() - 1) < .001 X = Geometric('X', Rational(1, 5)) Y = Geometric('Y', Rational(3, 10)) assert coskewness(X, X + Y, X + 2*Y).simplify() == sqrt(230)*Rational(81, 1150)
def test_bernoulli(): p, a, b, t = symbols('p a b t') X = Bernoulli('B', p, a, b) assert E(X) == a * p + b * (-p + 1) assert density(X)[a] == p assert density(X)[b] == 1 - p assert characteristic_function(X)( t) == p * exp(I * a * t) + (-p + 1) * exp(I * b * t) assert moment_generating_function(X)( t) == p * exp(a * t) + (-p + 1) * exp(b * t) X = Bernoulli('B', p, 1, 0) z = Symbol("z") assert E(X) == p assert simplify(variance(X)) == p * (1 - p) assert E(a * X + b) == a * E(X) + b assert simplify(variance(a * X + b)) == simplify(a**2 * variance(X)) assert quantile(X)(z) == Piecewise((nan, (z > 1) | (z < 0)), (0, z <= 1 - p), (1, z <= 1)) Y = Bernoulli('Y', Rational(1, 2)) assert median(Y) == FiniteSet(0, 1) Z = Bernoulli('Z', Rational(2, 3)) assert median(Z) == FiniteSet(1) raises(ValueError, lambda: Bernoulli('B', 1.5)) raises(ValueError, lambda: Bernoulli('B', -0.5)) #issue 8248 assert X.pspace.compute_expectation(1) == 1 p = Rational(1, 5) X = Binomial('X', 5, p) Y = Binomial('Y', 7, 2 * p) Z = Binomial('Z', 9, 3 * p) assert coskewness(Y + Z, X + Y, X + Z).simplify() == 0 assert coskewness(Y + 2*X + Z, X + 2*Y + Z, X + 2*Z + Y).simplify() == \ sqrt(1529)*Rational(12, 16819) assert coskewness(Y + 2*X + Z, X + 2*Y + Z, X + 2*Z + Y, X < 2).simplify() \ == -sqrt(357451121)*Rational(2812, 4646864573)