def test_binom_conf_interval():
# Test Wilson and Jeffreys interval for corner cases:
# Corner cases: k = 0, k = n, conf = 0., conf = 1.
n = 5
k = [0, 4, 5]
for conf in [0., 0.5, 1.]:
res = funcs.binom_conf_interval(k, n, conf=conf, interval='wilson')
assert ((res >= 0.) & (res <= 1.)).all()
res = funcs.binom_conf_interval(k, n, conf=conf, interval='jeffreys')
assert ((res >= 0.) & (res <= 1.)).all()
# Test Jeffreys interval accuracy against table in Brown et al. (2001).
# (See `binom_conf_interval` docstring for reference.)
k = [0, 1, 2, 3, 4]
n = 7
conf = 0.95
result = funcs.binom_conf_interval(k, n, conf=conf, interval='jeffreys')
table = np.array([[0.000, 0.016, 0.065, 0.139, 0.234],
[0.292, 0.501, 0.648, 0.766, 0.861]])
assert_allclose(result, table, atol=1.e-3, rtol=0.)
# Test scalar version
result = np.array([
funcs.binom_conf_interval(kval, n, conf=conf, interval='jeffreys')
for kval in k
]).transpose()
assert_allclose(result, table, atol=1.e-3, rtol=0.)
# Test flat
result = funcs.binom_conf_interval(k, n, conf=conf, interval='flat')
table = np.array([[0., 0.03185, 0.08523, 0.15701, 0.24486],
[0.36941, 0.52650, 0.65085, 0.75513, 0.84298]])
assert_allclose(result, table, atol=1.e-3, rtol=0.)
# Test scalar version
result = np.array([
funcs.binom_conf_interval(kval, n, conf=conf, interval='flat')
for kval in k
]).transpose()
assert_allclose(result, table, atol=1.e-3, rtol=0.)
# Test Wald interval
result = funcs.binom_conf_interval(0, 5, interval='wald')
assert_allclose(result, 0.) # conf interval is [0, 0] when k = 0
result = funcs.binom_conf_interval(5, 5, interval='wald')
assert_allclose(result, 1.) # conf interval is [1, 1] when k = n
result = funcs.binom_conf_interval(500,
1000,
conf=0.68269,
interval='wald')
assert_allclose(result[0], 0.5 - 0.5 / np.sqrt(1000.))
assert_allclose(result[1], 0.5 + 0.5 / np.sqrt(1000.))
# Test shapes
k = 3
n = 7
for interval in ['wald', 'wilson', 'jeffreys', 'flat']:
result = funcs.binom_conf_interval(k, n, interval=interval)
assert result.shape == (2, )
k = np.array(k)
for interval in ['wald', 'wilson', 'jeffreys', 'flat']:
result = funcs.binom_conf_interval(k, n, interval=interval)
assert result.shape == (2, )
n = np.array(n)
for interval in ['wald', 'wilson', 'jeffreys', 'flat']:
result = funcs.binom_conf_interval(k, n, interval=interval)
assert result.shape == (2, )
k = np.array([1, 3, 5])
for interval in ['wald', 'wilson', 'jeffreys', 'flat']:
result = funcs.binom_conf_interval(k, n, interval=interval)
assert result.shape == (2, 3)
n = np.array([5, 5, 5])
for interval in ['wald', 'wilson', 'jeffreys', 'flat']:
result = funcs.binom_conf_interval(k, n, interval=interval)
assert result.shape == (2, 3)
def test_binom_conf_interval():
# Test Wilson and Jeffreys interval for corner cases:
# Corner cases: k = 0, k = n, conf = 0., conf = 1.
n = 5
k = [0, 4, 5]
for conf in [0., 0.5, 1.]:
res = funcs.binom_conf_interval(k, n, conf=conf, interval='wilson')
assert ((res >= 0.) & (res <= 1.)).all()
res = funcs.binom_conf_interval(k, n, conf=conf, interval='jeffreys')
assert ((res >= 0.) & (res <= 1.)).all()
# Test Jeffreys interval accuracy against table in Brown et al. (2001).
# (See `binom_conf_interval` docstring for reference.)
k = [0, 1, 2, 3, 4]
n = 7
conf = 0.95
result = funcs.binom_conf_interval(k, n, conf=conf, interval='jeffreys')
table = np.array([[0.000, 0.016, 0.065, 0.139, 0.234],
[0.292, 0.501, 0.648, 0.766, 0.861]])
assert_allclose(result, table, atol=1.e-3, rtol=0.)
# Test scalar version
result = np.array([funcs.binom_conf_interval(kval, n, conf=conf,
interval='jeffreys')
for kval in k]).transpose()
assert_allclose(result, table, atol=1.e-3, rtol=0.)
# Test flat
result = funcs.binom_conf_interval(k, n, conf=conf, interval='flat')
table = np.array([[0., 0.03185, 0.08523, 0.15701, 0.24486],
[0.36941, 0.52650, 0.65085, 0.75513, 0.84298]])
assert_allclose(result, table, atol=1.e-3, rtol=0.)
# Test scalar version
result = np.array([funcs.binom_conf_interval(kval, n, conf=conf,
interval='flat')
for kval in k]).transpose()
assert_allclose(result, table, atol=1.e-3, rtol=0.)
# Test Wald interval
result = funcs.binom_conf_interval(0, 5, interval='wald')
assert_allclose(result, 0.) # conf interval is [0, 0] when k = 0
result = funcs.binom_conf_interval(5, 5, interval='wald')
assert_allclose(result, 1.) # conf interval is [1, 1] when k = n
result = funcs.binom_conf_interval(500, 1000, conf=0.68269,
interval='wald')
assert_allclose(result[0], 0.5 - 0.5 / np.sqrt(1000.))
assert_allclose(result[1], 0.5 + 0.5 / np.sqrt(1000.))
# Test shapes
k = 3
n = 7
for interval in ['wald', 'wilson', 'jeffreys', 'flat']:
result = funcs.binom_conf_interval(k, n, interval=interval)
assert result.shape == (2,)
k = np.array(k)
for interval in ['wald', 'wilson', 'jeffreys', 'flat']:
result = funcs.binom_conf_interval(k, n, interval=interval)
assert result.shape == (2,)
n = np.array(n)
for interval in ['wald', 'wilson', 'jeffreys', 'flat']:
result = funcs.binom_conf_interval(k, n, interval=interval)
assert result.shape == (2,)
k = np.array([1, 3, 5])
for interval in ['wald', 'wilson', 'jeffreys', 'flat']:
result = funcs.binom_conf_interval(k, n, interval=interval)
assert result.shape == (2, 3)
n = np.array([5, 5, 5])
for interval in ['wald', 'wilson', 'jeffreys', 'flat']:
result = funcs.binom_conf_interval(k, n, interval=interval)
assert result.shape == (2, 3)