def compute_pref(mu1, mu2, sigma1_sq, sigma2_sq, margin):
if mu1 < mu2:
raise "mu1 must be greater than mu2"
mu0 = mu1 - mu2
sigma0_sq = sigma1_sq + sigma2_sq
sigma0 = math.sqrt(sigma0_sq)
N = Normal(mu0, sigma0)
prob_win = N.probability(margin, oo).evalf()
prob_lost = N.probability(-oo, 0).evalf()
prob_draw = 1.- (prob_lost + prob_win)
return prob_win, prob_draw, prob_lost
def compute_pref(mu1, mu2, sigma1_sq, sigma2_sq, margin):
if mu1 < mu2:
raise "mu1 must be greater than mu2"
mu0 = mu1 - mu2
sigma0_sq = sigma1_sq + sigma2_sq
sigma0 = math.sqrt(sigma0_sq)
N = Normal(mu0, sigma0)
prob_win = N.probability(margin, oo).evalf()
prob_lost = N.probability(-oo, 0).evalf()
prob_draw = 1. - (prob_lost + prob_win)
return prob_win, prob_draw, prob_lost
def test_normal():
dps, mp.dps = mp.dps, 20
N = Normal(0, 1)
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 operator.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.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
