def test_fit():
import random
random.seed(1234)
n = Normal.fit(Uniform.fit(Normal(2, 1.5).random(1000)))
#print n.mean
#print n.stddev
assert abs(n.mean - 2) < 0.3
assert abs(n.stddev - 1.5) < 0.3
n = Normal.fit([1, 2, 3, 4, 5])
assert n.mean == 3
assert n.stddev == sqrt(2)
n = Uniform.fit([1, 2, 3, 4, 5])
assert n.mean == 3
assert n.stddev == sqrt(2)
def test_fit():
import random
random.seed(1234)
n = Normal.fit(Uniform.fit(Normal(2, 1.5).random(1000)))
#print n.mean
#print n.stddev
assert abs(n.mean - 2) < 0.3
assert abs(n.stddev - 1.5) < 0.3
n = Normal.fit([1, 2, 3, 4, 5])
assert n.mean == 3
assert n.stddev == sqrt(2)
n = Uniform.fit([1, 2, 3, 4, 5])
assert n.mean == 3
assert n.stddev == sqrt(2)
def test_RandomDomain():
from sympy.stats import Normal, Die, Exponential, pspace, where
X = Normal('x1', 0, 1)
assert str(where(X > 0)) == "Domain: 0 < x1"
D = Die('d1', 6)
assert str(where(D > 4)) == "Domain: Or(d1 == 5, d1 == 6)"
A = Exponential('a', 1)
B = Exponential('b', 1)
assert str(pspace(Tuple(A, B)).domain) == "Domain: And(0 <= a, 0 <= b)"
def test_RandomDomain():
from sympy.stats import Normal, Die, Exponential, pspace, Where
X = Normal(0, 1, symbol=Symbol('x1'))
assert str(Where(X > 0)) == "Domain: 0 < x1"
D = Die(6, symbol=Symbol('d1'))
assert str(Where(D > 4)) == "Domain: Or(d1 == 5, d1 == 6)"
A = Exponential(1, symbol=Symbol('a'))
B = Exponential(1, symbol=Symbol('b'))
assert str(pspace(Tuple(A, B)).domain) == "Domain: And(0 <= a, 0 <= b)"
def test_printing():
assert str(Normal(x + y, z)) == "Normal(x + y, z)"
assert str(Sample([x, y, 1])) in [
"Sample([x, y, 1])",
"Sample([y, 1, x])",
"Sample([1, x, y])",
"Sample([y, x, 1])",
"Sample([x, 1, y])",
"Sample([1, y, x])",
]
assert str(Uniform(x, y)) == "Uniform(x, y)"
assert str(Uniform(x + y, y)) == "Uniform(x + y, y)"
def test_Normal():
assert str(Normal(x + y, z)) == "Normal(x + y, z)"
def test_statistics():
x = Symbol("x")
y = Symbol("y")
for c in (ContinuousProbability, ContinuousProbability(), Normal,
Normal(x, y), Sample, Sample([1, 3, 4]), Uniform, Uniform(x, y)):
check(c)
def test_normal():
dps, mp.dps = mp.dps, 20
N = Normal(0, 1)
assert N.random()
assert N.mean == 0
assert N.variance == 1
assert N.probability(-1, 1) == erf(1/sqrt(2))
assert N.probability(-1, 0) == erf(1/sqrt(2))/2
N = Normal(2, 4)
assert N.mean == 2
assert N.variance == 16
assert N.confidence(1) == (-oo, oo)
assert N.probability(1, 3) == erf(1/sqrt(32))
assert N.pdf(1).evalf() == (exp(Rational(-1, 32)) / (4*sqrt(2*pi))).evalf()
for p in [0.1, 0.3, 0.7, 0.9, 0.995]:
a, b = N.confidence(p)
assert abs(float(N.probability(a, b).evalf()) - p) < 1e-10
N = Normal(0, 2/sqrt(2*pi))
assert N.pdf(0) == Rational(1, 2)
mp.dps = dps
def test_normal():
dps, mp.dps = mp.dps, 20
N = Normal(0, 1)
assert N.random()
assert N.mean == 0
assert N.variance == 1
assert N.probability(-1, 1) == erf(1 / sqrt(2))
assert N.probability(-1, 0) == erf(1 / sqrt(2)) / 2
N = Normal(2, 4)
assert N.mean == 2
assert N.variance == 16
assert N.confidence(1) == (-oo, oo)
assert N.probability(1, 3) == erf(1 / sqrt(32))
assert N.pdf(1).evalf() == (exp(Rational(-1, 32)) /
(4 * sqrt(2 * pi))).evalf()
for p in [0.1, 0.3, 0.7, 0.9, 0.995]:
a, b = N.confidence(p)
assert abs(float(N.probability(a, b).evalf()) - p) < 1e-10
N = Normal(0, 2 / sqrt(2 * pi))
assert N.pdf(0) == Rational(1, 2)
mp.dps = dps
def test_pickling():
for c in (ContinuousProbability, ContinuousProbability(), Normal,
Normal(x, y), Sample, Sample([1, 3, 4]), Uniform, Uniform(x, y)):
check(c)
