def testPoisson(self):
"""Check output on a continuous Poisson-like distribution"""
l = 4 #Expected number of counts
poiss = lambda k: l**k * math.exp(-l) / scipy.special.gamma(k + 1)
mean = lambda x: sum(x) / len(x)
if self.long_test:
poiss_values = toolbox.dist_to_list(poiss, 5000, 0, 100)
(ci_low, ci_high) = poppy.boots_ci(poiss_values,
50000,
95.0,
mean,
seed=0)
#IF this were normal (which it isn't), expected confidence interval
#3.94456 - 4.05544, in reality should be skewed right
self.assertAlmostEqual(3.97171801164, ci_low, places=10)
self.assertAlmostEqual(4.08051711605, ci_high, places=10)
else:
poiss_values = toolbox.dist_to_list(poiss, 100, 0, 100)
(ci_low, ci_high) = poppy.boots_ci(poiss_values,
100,
95.0,
mean,
seed=0)
#'Expected' 3.608 - 4.392
self.assertAlmostEqual(3.57505503117, ci_low, places=10)
self.assertAlmostEqual(4.4100232162, ci_high, places=10)
def testLogNormal(self):
"""Check output on a LogNormal"""
lnorm = lambda x: math.exp(-1*(math.log(x) - 5.1)**2./(2*0.3**2.) ) \
/ (x*math.sqrt(2*math.pi) * 0.3)
if self.long_test:
dist_values = toolbox.dist_to_list(lnorm, 5000, min=0)
(ci_low, ci_high) = poppy.boots_ci(dist_values,
50000,
95.0,
numpy.median,
seed=0)
#confidence interval is given as [exp(mu-sigma*q), exp(mu+sigma*q)]
#where q is the (1 - alpha/2) quantile of the standard normal distr.
#Here, the theoretical median is 164.022 (6 s.f.)
self.assertAlmostEqual(162.31603275984526, ci_low, places=10)
self.assertAlmostEqual(165.73324112594128, ci_high, places=10)
else:
dist_values = toolbox.dist_to_list(lnorm, 100, min=0)
(ci_low, ci_high) = poppy.boots_ci(dist_values,
100,
95.0,
numpy.median,
seed=0)
#TODO: the CI for lognorms should be calculated by the given form
#currently this is just taken from the test code output
#after the distributions have been calculated. The values do fit
#with the theoretical median though...
self.assertAlmostEqual(152.6079463660717, ci_low, places=10)
self.assertAlmostEqual(174.61664971746504, ci_high, places=10)
def testGaussian(self):
"""Check output on a Gaussian"""
gauss = lambda x: math.exp(-(x ** 2) / (2 * 5 ** 2)) / \
(5 * math.sqrt(2 * math.pi))
mean = lambda x: sum(x) / len(x)
if self.long_test:
gauss_values = toolbox.dist_to_list(gauss, 5000)
(ci_low, ci_high, prc) = poppy.boots_ci(gauss_values,
50000,
95.0,
mean,
seed=0,
target=-0.138)
#standard error on the mean for 5000 samples, standard dev 5 is
#0.0707, 95% confidence interval is 1.96 standard dev or
#0.13859292911256332 (+/-)
self.assertAlmostEqual(-0.138373060749, ci_low, places=10)
self.assertAlmostEqual(0.137630863579, ci_high, places=10)
self.assertAlmostEqual(97.453789371746154, prc, places=10)
else:
gauss_values = toolbox.dist_to_list(gauss, 100)
(ci_low, ci_high, prc) = poppy.boots_ci(gauss_values,
100,
95.0,
mean,
seed=0,
target=-1.04)
#for 100 samples, stderr is 0.5, 95% is +/- 0.98
self.assertAlmostEqual(-1.03977357727, ci_low, places=10)
self.assertAlmostEqual(0.914472603387, ci_high, places=10)
self.assertAlmostEqual(97.502939756605045, prc, places=10)
def testDistToList(self):
"""Convert probability distribution to list of values"""
inputs = [[lambda x: x, 10, 0, 10],
[lambda x: numpy.exp(-(x ** 2) / (2 * 5 ** 2)) / \
(5 * numpy.sqrt(2 * numpy.pi)), 20],
]
outputs = [[2.2360679774998005,
3.8729833462074126,
5.0,
5.91607978309959,
6.708203932499401,
7.416198487095684,
8.06225774829855,
8.66025403784434,
9.219544457292841,
9.746794344808976],
[-9.799819946289062, -7.197657585144043,
-5.751746901776642, -4.672946454957128,
-3.777075132355094, -2.9888006299734116,
-2.268810950219631, -1.5931968204677105,
-0.9455921351909637, -0.31353388726711273,
0.3135339021682739, 0.9455921053886414,
1.5931968688964844, 2.268810987472534,
2.988800525665283, 3.7770752906799316,
4.672946453094482, 5.751747131347656,
7.197657346725464, 9.799819946289062]
]
for (input, output) in zip(inputs, outputs):
numpy.testing.assert_almost_equal(output, tb.dist_to_list(*input))
def testDistToList(self):
"""Convert probability distribution to list of values"""
inputs = [[lambda x: x, 10, 0, 10],
[lambda x: numpy.exp(-(x ** 2) / (2 * 5 ** 2)) / \
(5 * numpy.sqrt(2 * numpy.pi)), 20],
]
outputs = [[2.2360679774998005,
3.8729833462074126,
5.0,
5.91607978309959,
6.708203932499401,
7.416198487095684,
8.06225774829855,
8.66025403784434,
9.219544457292841,
9.746794344808976],
[-9.799819946289062, -7.197657585144043,
-5.751746901776642, -4.672946454957128,
-3.777075132355094, -2.9888006299734116,
-2.268810950219631, -1.5931968204677105,
-0.9455921351909637, -0.31353388726711273,
0.3135339021682739, 0.9455921053886414,
1.5931968688964844, 2.268810987472534,
2.988800525665283, 3.7770752906799316,
4.672946453094482, 5.751747131347656,
7.197657346725464, 9.799819946289062]
]
for (input, output) in zip(inputs, outputs):
numpy.testing.assert_almost_equal(output, tb.dist_to_list(*input))
def testPoisson(self):
"""Check output on a continuous Poisson-like distribution"""
l = 4 #Expected number of counts
poiss = lambda k: l **k * math.exp(-l) / scipy.special.gamma(k + 1)
mean = lambda x: sum(x) / len(x)
if self.long_test:
poiss_values = toolbox.dist_to_list(poiss, 5000, 0, 100)
(ci_low, ci_high) = poppy.boots_ci(poiss_values, 50000, 95.0, mean,
seed=0)
#IF this were normal (which it isn't), expected confidence interval
#3.94456 - 4.05544, in reality should be skewed right
self.assertAlmostEqual(3.97171801164, ci_low, places=10)
self.assertAlmostEqual(4.08051711605, ci_high, places=10)
else:
poiss_values = toolbox.dist_to_list(poiss, 100, 0, 100)
(ci_low, ci_high) = poppy.boots_ci(poiss_values, 100, 95.0, mean,
seed=0)
#'Expected' 3.608 - 4.392
self.assertAlmostEqual(3.57505503117, ci_low, places=10)
self.assertAlmostEqual(4.4100232162, ci_high, places=10)
def testGaussian(self):
"""Check output on a Gaussian"""
gauss = lambda x: math.exp(-(x ** 2) / (2 * 5 ** 2)) / \
(5 * math.sqrt(2 * math.pi))
mean = lambda x: sum(x) / len(x)
if self.long_test:
gauss_values = toolbox.dist_to_list(gauss, 5000)
(ci_low, ci_high, prc) = poppy.boots_ci(
gauss_values, 50000, 95.0, mean, seed=0, target=-0.138)
#standard error on the mean for 5000 samples, standard dev 5 is
#0.0707, 95% confidence interval is 1.96 standard dev or
#0.13859292911256332 (+/-)
self.assertAlmostEqual(-0.138373060749, ci_low, places=10)
self.assertAlmostEqual(0.137630863579, ci_high, places=10)
self.assertAlmostEqual(97.453789371746154, prc, places=10)
else:
gauss_values = toolbox.dist_to_list(gauss, 100)
(ci_low, ci_high, prc) = poppy.boots_ci(
gauss_values, 100, 95.0, mean, seed=0, target=-1.04)
#for 100 samples, stderr is 0.5, 95% is +/- 0.98
self.assertAlmostEqual(-1.03977357727, ci_low, places=10)
self.assertAlmostEqual(0.914472603387, ci_high, places=10)
self.assertAlmostEqual(97.502939756605045, prc, places=10)
def testLogNormal(self):
"""Check output on a LogNormal"""
lnorm = lambda x: math.exp(-1*(math.log(x) - 5.1)**2./(2*0.3**2.) ) \
/ (x*math.sqrt(2*math.pi) * 0.3)
if self.long_test:
dist_values = toolbox.dist_to_list(lnorm, 5000, min=0)
(ci_low, ci_high) = poppy.boots_ci(dist_values, 50000, 95.0,
numpy.median, seed=0)
#confidence interval is given as [exp(mu-sigma*q), exp(mu+sigma*q)]
#where q is the (1 - alpha/2) quantile of the standard normal distr.
#Here, the theoretical median is 164.022 (6 s.f.)
self.assertAlmostEqual(162.31603275984526, ci_low, places=10)
self.assertAlmostEqual(165.73324112594128, ci_high, places=10)
else:
dist_values = toolbox.dist_to_list(lnorm, 100, min=0)
(ci_low, ci_high) = poppy.boots_ci(dist_values, 100, 95.0,
numpy.median, seed=0)
#TODO: the CI for lognorms should be calculated by the given form
#currently this is just taken from the test code output
#after the distributions have been calculated. The values do fit
#with the theoretical median though...
self.assertAlmostEqual(152.6079463660717, ci_low, places=10)
self.assertAlmostEqual(174.61664971746504, ci_high, places=10)
