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from sympy.concrete.summations import Sum |
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from sympy.core.add import Add |
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from sympy.core.mul import Mul |
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from sympy.core.numbers import (Integer, oo, pi) |
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from sympy.core.power import Pow |
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from sympy.core.relational import (Eq, Ne) |
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from sympy.core.symbol import (Dummy, Symbol, symbols) |
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from sympy.functions.combinatorial.factorials import factorial |
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from sympy.functions.elementary.exponential import exp |
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from sympy.functions.elementary.miscellaneous import sqrt |
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from sympy.functions.elementary.piecewise import Piecewise |
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from sympy.functions.special.delta_functions import DiracDelta |
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from sympy.functions.special.gamma_functions import gamma |
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from sympy.integrals.integrals import Integral |
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from sympy.simplify.simplify import simplify |
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from sympy.tensor.indexed import (Indexed, IndexedBase) |
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from sympy.functions.elementary.piecewise import ExprCondPair |
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from sympy.stats import (Poisson, Beta, Exponential, P, |
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Multinomial, MultivariateBeta) |
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from sympy.stats.crv_types import Normal |
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from sympy.stats.drv_types import PoissonDistribution |
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from sympy.stats.compound_rv import CompoundPSpace, CompoundDistribution |
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from sympy.stats.joint_rv import MarginalDistribution |
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from sympy.stats.rv import pspace, density |
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from sympy.testing.pytest import ignore_warnings |
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def test_density(): |
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x = Symbol('x') |
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l = Symbol('l', positive=True) |
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rate = Beta(l, 2, 3) |
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X = Poisson(x, rate) |
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assert isinstance(pspace(X), CompoundPSpace) |
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assert density(X, Eq(rate, rate.symbol)) == PoissonDistribution(l) |
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N1 = Normal('N1', 0, 1) |
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N2 = Normal('N2', N1, 2) |
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assert density(N2)(0).doit() == sqrt(10)/(10*sqrt(pi)) |
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assert simplify(density(N2, Eq(N1, 1))(x)) == \ |
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sqrt(2)*exp(-(x - 1)**2/8)/(4*sqrt(pi)) |
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assert simplify(density(N2)(x)) == sqrt(10)*exp(-x**2/10)/(10*sqrt(pi)) |
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def test_MarginalDistribution(): |
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a1, p1, p2 = symbols('a1 p1 p2', positive=True) |
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C = Multinomial('C', 2, p1, p2) |
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B = MultivariateBeta('B', a1, C[0]) |
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MGR = MarginalDistribution(B, (C[0],)) |
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mgrc = Mul(Symbol('B'), Piecewise(ExprCondPair(Mul(Integer(2), |
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Pow(Symbol('p1', positive=True), Indexed(IndexedBase(Symbol('C')), |
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Integer(0))), Pow(Symbol('p2', positive=True), |
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Indexed(IndexedBase(Symbol('C')), Integer(1))), |
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Pow(factorial(Indexed(IndexedBase(Symbol('C')), Integer(0))), Integer(-1)), |
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Pow(factorial(Indexed(IndexedBase(Symbol('C')), Integer(1))), Integer(-1))), |
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Eq(Add(Indexed(IndexedBase(Symbol('C')), Integer(0)), |
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Indexed(IndexedBase(Symbol('C')), Integer(1))), Integer(2))), |
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ExprCondPair(Integer(0), True)), Pow(gamma(Symbol('a1', positive=True)), |
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Integer(-1)), gamma(Add(Symbol('a1', positive=True), |
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Indexed(IndexedBase(Symbol('C')), Integer(0)))), |
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Pow(gamma(Indexed(IndexedBase(Symbol('C')), Integer(0))), Integer(-1)), |
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Pow(Indexed(IndexedBase(Symbol('B')), Integer(0)), |
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Add(Symbol('a1', positive=True), Integer(-1))), |
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Pow(Indexed(IndexedBase(Symbol('B')), Integer(1)), |
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Add(Indexed(IndexedBase(Symbol('C')), Integer(0)), Integer(-1)))) |
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assert MGR(C) == mgrc |
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def test_compound_distribution(): |
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Y = Poisson('Y', 1) |
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Z = Poisson('Z', Y) |
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assert isinstance(pspace(Z), CompoundPSpace) |
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assert isinstance(pspace(Z).distribution, CompoundDistribution) |
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assert Z.pspace.distribution.pdf(1).doit() == exp(-2)*exp(exp(-1)) |
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def test_mix_expression(): |
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Y, E = Poisson('Y', 1), Exponential('E', 1) |
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k = Dummy('k') |
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expr1 = Integral(Sum(exp(-1)*Integral(exp(-k)*DiracDelta(k - 2), (k, 0, oo) |
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)/factorial(k), (k, 0, oo)), (k, -oo, 0)) |
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expr2 = Integral(Sum(exp(-1)*Integral(exp(-k)*DiracDelta(k - 2), (k, 0, oo) |
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)/factorial(k), (k, 0, oo)), (k, 0, oo)) |
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assert P(Eq(Y + E, 1)) == 0 |
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assert P(Ne(Y + E, 2)) == 1 |
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with ignore_warnings(UserWarning): |
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assert P(E + Y < 2, evaluate=False).rewrite(Integral).dummy_eq(expr1) |
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assert P(E + Y > 2, evaluate=False).rewrite(Integral).dummy_eq(expr2) |
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