def test_long_precomputed_cdf():
x = symbols("x", real=True, finite=True)
distribs = [
Arcsin("A", -5, 9),
Dagum("D", 4, 10, 3),
Erlang("E", 14, 5),
Frechet("F", 2, 6, -3),
Gamma("G", 2, 7),
GammaInverse("GI", 3, 5),
Kumaraswamy("K", 6, 8),
Laplace("LA", -5, 4),
Logistic("L", -6, 7),
Nakagami("N", 2, 7),
StudentT("S", 4)
]
for distr in distribs:
for _ in range(5):
assert tn(diff(cdf(distr)(x), x),
density(distr)(x),
x,
a=0,
b=0,
c=1,
d=0)
US = UniformSum("US", 5)
pdf01 = density(US)(x).subs(floor(x), 0).doit() # pdf on (0, 1)
cdf01 = cdf(US, evaluate=False)(x).subs(floor(x),
0).doit() # cdf on (0, 1)
assert tn(diff(cdf01, x), pdf01, x, a=0, b=0, c=1, d=0)
def test_arcsin():
a = Symbol("a", real=True)
b = Symbol("b", real=True)
x = Symbol("x")
X = Arcsin(a, b, symbol=x)
assert density(X) == Lambda(_x, 1 / (pi * sqrt((-_x + b) * (_x - a))))
def test_arcsin():
from sympy import asin
a = Symbol("a", real=True)
b = Symbol("b", real=True)
X = Arcsin('x', a, b)
assert density(X)(x) == 1/(pi*sqrt((-x + b)*(x - a)))
assert cdf(X)(x) == Piecewise((0, a > x),
(2*asin(sqrt((-a + x)/(-a + b)))/pi, b >= x),
(1, True))
def test_arcsin():
a = Symbol("a", real=True)
b = Symbol("b", real=True)
X = Arcsin('x', a, b)
assert density(X)(x) == 1/(pi*sqrt((-x + b)*(x - a)))
def test_arcsin():
a = Symbol("a", real=True)
b = Symbol("b", real=True)
X = Arcsin('x', a, b)
assert density(X) == Lambda(_x, 1 / (pi * sqrt((-_x + b) * (_x - a))))