def test_nakagami():
mu = Symbol("mu", positive=True)
omega = Symbol("omega", positive=True)
X = Nakagami('x', mu, omega)
assert density(X)(x) == (2*x**(2*mu - 1)*mu**mu*omega**(-mu)
*exp(-x**2*mu/omega)/gamma(mu))
assert simplify(E(X)) == (sqrt(mu)*sqrt(omega)
*gamma(mu + S.Half)/gamma(mu + 1))
assert simplify(variance(X)) == (
omega - omega*gamma(mu + S.Half)**2/(gamma(mu)*gamma(mu + 1)))
assert cdf(X)(x) == Piecewise(
(lowergamma(mu, mu*x**2/omega)/gamma(mu), x > 0),
(0, True))
X = Nakagami('x',1 ,1)
assert median(X) == FiniteSet(sqrt(log(2)))
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_nakagami():
mu = Symbol("mu", positive=True)
omega = Symbol("omega", positive=True)
X = Nakagami('x', mu, omega)
assert density(X)(x) == (2*x**(2*mu - 1)*mu**mu*omega**(-mu)
*exp(-x**2*mu/omega)/gamma(mu))
assert simplify(E(X, meijerg=True)) == (sqrt(mu)*sqrt(omega)
*gamma(mu + S.Half)/gamma(mu + 1))
assert simplify(variance(X, meijerg=True)) == (
omega - omega*gamma(mu + S(1)/2)**2/(gamma(mu)*gamma(mu + 1)))
def test_nakagami():
mu = Symbol("mu", positive=True)
omega = Symbol("omega", positive=True)
X = Nakagami('x', mu, omega)
assert density(X) == (Lambda(_x, 2*_x**(2*mu - 1)*mu**mu*omega**(-mu)
*exp(-_x**2*mu/omega)/gamma(mu)))
assert simplify(E(X, meijerg=True)) == (sqrt(mu)*sqrt(omega)
*gamma(mu + S.Half)/gamma(mu + 1))
assert (simplify(variance(X, meijerg=True)) ==
(omega*(gamma(mu)*gamma(mu + 1)
- gamma(mu + S.Half)**2)/(gamma(mu)*gamma(mu + 1))))