def normal_dist(mu=100, sigma=15):
"""
mainfunc
"""
dist = Normal(mu,sigma)
dist_cdf = dist.cdf(x)
sympy.Plot(dist_cdf)
pass
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
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_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
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
def getStdDev(distance, confidence, x=Normal(0, 1)):
"Distance = end point - mean"
confidenceDistance = x.confidence(confidence)[1]
stddev = confidenceDistance * distance
return stddev