예제 #1
0
def test_maxwell():
    a = Symbol("a", positive=True)

    X = Maxwell('x', a)

    assert density(X)(x) == (sqrt(2)*x**2*exp(-x**2/(2*a**2))/
        (sqrt(pi)*a**3))
    assert E(X) == 2*sqrt(2)*a/sqrt(pi)
    assert simplify(variance(X)) == a**2*(-8 + 3*pi)/pi
예제 #2
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def test_maxwell():
    a = Symbol("a", positive=True)

    X = Maxwell('x', a)

    assert density(X)(x) == (sqrt(2)*x**2*exp(-x**2/(2*a**2))/
        (sqrt(pi)*a**3))
    assert E(X) == 2*sqrt(2)*a/sqrt(pi)
    assert variance(X) == -8*a**2/pi + 3*a**2
    assert cdf(X)(x) == erf(sqrt(2)*x/(2*a)) - sqrt(2)*x*exp(-x**2/(2*a**2))/(sqrt(pi)*a)
    assert diff(cdf(X)(x), x) == density(X)(x)
예제 #3
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def test_maxwell():
    a = Symbol("a", positive=True)
    x = Symbol("x")

    X = Maxwell(a, symbol=x)

    assert density(X) == (Lambda(
        _x,
        sqrt(2) * _x**2 * exp(-_x**2 / (2 * a**2)) / (sqrt(pi) * a**3)))
    assert E(X) == 2 * sqrt(2) * a / sqrt(pi)
    assert simplify(variance(X)) == a**2 * (-8 + 3 * pi) / pi