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))
raises(ValueError, lambda: Bernoulli("B", 1.5))
raises(ValueError, lambda: Bernoulli("B", -0.5))
# issue 8248
assert X.pspace.compute_expectation(1) == 1
def test_bernoulli():
p, a, b = symbols('p a b')
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
X = Bernoulli('B', p, 1, 0)
assert E(X) == p
assert variance(X) == -p**2 + p
E(a * X + b) == a * E(X) + b
variance(a * X + b) == a**2 * variance(X)
def test_bernoulli():
p, a, b = symbols('p a b')
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
X = Bernoulli('B', p, 1, 0)
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))
def test_bernoulli():
p, a, b = symbols('p a b')
X = Bernoulli(p, a, b, symbol='B')
assert E(X) == a * p + b * (-p + 1)
assert Density(X)[a] == p
assert Density(X)[b] == 1 - p
X = Bernoulli(p, 1, 0, symbol='B')
assert E(X) == p
assert Var(X) == -p**2 + p
E(a * X + b) == a * E(X) + b
Var(a * X + b) == a**2 * Var(X)
def test_sample_scipy():
distribs_scipy = [
FiniteRV('F', {
1: S.Half,
2: Rational(1, 4),
3: Rational(1, 4)
}),
DiscreteUniform("Y", list(range(5))),
Die("D"),
Bernoulli("Be", 0.3),
Binomial("Bi", 5, 0.4),
BetaBinomial("Bb", 2, 1, 1),
Hypergeometric("H", 1, 1, 1),
Rademacher("R")
]
size = 3
scipy = import_module('scipy')
if not scipy:
skip('Scipy not installed. Abort tests for _sample_scipy.')
else:
for X in distribs_scipy:
samps = sample(X, size=size)
samps2 = sample(X, size=(2, 2))
for sam in samps:
assert sam in X.pspace.domain.set
for i in range(2):
for j in range(2):
assert samps2[i][j] in X.pspace.domain.set
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)
X = Bernoulli('B', p, 1, 0)
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))
def test_sample_scipy():
distribs_scipy = [
FiniteRV('F', {1: S.Half, 2: Rational(1, 4), 3: Rational(1, 4)}),
DiscreteUniform("Y", list(range(5))),
Die("D"),
Bernoulli("Be", 0.3),
Binomial("Bi", 5, 0.4),
BetaBinomial("Bb", 2, 1, 1),
Hypergeometric("H", 1, 1, 1),
Rademacher("R")
]
size = 3
numsamples = 5
scipy = import_module('scipy')
if not scipy:
skip('Scipy not installed. Abort tests for _sample_scipy.')
else:
with ignore_warnings(UserWarning): ### TODO: Restore tests once warnings are removed
h_sample = list(sample(Hypergeometric("H", 1, 1, 1), size=size, numsamples=numsamples))
assert len(h_sample) == numsamples
for X in distribs_scipy:
samps = next(sample(X, size=size))
samps2 = next(sample(X, size=(2, 2)))
for sam in samps:
assert sam in X.pspace.domain.set
for i in range(2):
for j in range(2):
assert samps2[i][j] in X.pspace.domain.set
def test_bernoulli_CompoundDist():
X = Beta('X', 1, 2)
Y = Bernoulli('Y', X)
assert density(Y).dict == {0: S(2)/3, 1: S(1)/3}
assert E(Y) == P(Eq(Y, 1)) == S(1)/3
assert variance(Y) == S(2)/9
assert cdf(Y) == {0: S(2)/3, 1: 1}
# test issue 8128
a = Bernoulli('a', S(1)/2)
b = Bernoulli('b', a)
assert density(b).dict == {0: S(1)/2, 1: S(1)/2}
assert P(b > 0.5) == S(1)/2
X = Uniform('X', 0, 1)
Y = Bernoulli('Y', X)
assert E(Y) == S(1)/2
assert P(Eq(Y, 1)) == E(Y)
def test_density_call():
x = Bernoulli('x', p)
d = density(x)
assert d(0) == 1 - p
assert d(S.Zero) == 1 - p
assert d(5) == 0
assert 0 in d
assert 5 not in d
assert d(S(0)) == d[S(0)]
def test_density_call():
from sympy.abc import p
x = Bernoulli('x', p)
d = density(x)
assert d(0) == 1 - p
assert d(S.Zero) == 1 - p
assert d(5) == 0
assert 0 in d
assert 5 not in d
assert d(S.Zero) == d[S.Zero]
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)
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))
raises(ValueError, lambda: Bernoulli('B', 1.5))
raises(ValueError, lambda: Bernoulli('B', -0.5))
def test_symbolic_conditions():
B = Bernoulli('B', S(1) / 4)
D = Die('D', 4)
b, n = symbols('b, n')
Y = P(Eq(B, b))
Z = E(D > n)
assert Y == \
Piecewise((S(1)/4, Eq(b, 1)), (0, True)) + \
Piecewise((S(3)/4, Eq(b, 0)), (0, True))
assert Z == \
Piecewise((S(1)/4, n < 1), (0, True)) + Piecewise((S(1)/2, n < 2), (0, True)) + \
Piecewise((S(3)/4, n < 3), (0, True)) + Piecewise((S(1), n < 4), (0, True))
def test_symbolic_conditions():
B = Bernoulli('B', Rational(1, 4))
D = Die('D', 4)
b, n = symbols('b, n')
Y = P(Eq(B, b))
Z = E(D > n)
assert Y == \
Piecewise((Rational(1, 4), Eq(b, 1)), (0, True)) + \
Piecewise((Rational(3, 4), Eq(b, 0)), (0, True))
assert Z == \
Piecewise((Rational(1, 4), n < 1), (0, True)) + Piecewise((S.Half, n < 2), (0, True)) + \
Piecewise((Rational(3, 4), n < 3), (0, True)) + Piecewise((S.One, n < 4), (0, True))
def test_sample_pymc3():
distribs_pymc3 = [Bernoulli('B', 0.2), Binomial('N', 5, 0.4)]
size = 3
pymc3 = import_module('pymc3')
if not pymc3:
skip('PyMC3 is not installed. Abort tests for _sample_pymc3.')
else:
for X in distribs_pymc3:
samps = sample(X, size=size, library='pymc3')
for sam in samps:
assert sam in X.pspace.domain.set
raises(NotImplementedError, lambda:
(sample(Die("D"), library='pymc3')))
def test_sample_pymc3():
distribs_pymc3 = [Bernoulli('B', 0.2), Binomial('N', 5, 0.4)]
size = 3
pymc3 = import_module('pymc3')
if not pymc3:
skip('PyMC3 is not installed. Abort tests for _sample_pymc3.')
else:
with ignore_warnings(
UserWarning
): ### TODO: Restore tests once warnings are removed
for X in distribs_pymc3:
samps = next(sample(X, size=size, library='pymc3'))
for sam in samps:
assert sam in X.pspace.domain.set
raises(NotImplementedError,
lambda: next(sample(Die("D"), library='pymc3')))
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)
def test_density_call():
x = Bernoulli('x', p)
d = density(x)
assert d(0) == 1 - p
import numpy as np
import pandas as pd
from scipy.stats import bernoulli
n, p = 1, .33 # n = coins flipped, p = prob of success
s = np.random.binomial(3000, 0.50)
from sympy.stats import Bernoulli, sample_iter
list(sample_iter(Bernoulli('X', 0.8),
numsamples=10)) # p = 0.8 and nsamples=10
