def test_fit_normal_to_confidence_interval(self):
"""fit_normal_to_confidence_interval should return a mean and variance given CI"""
#Lets use a normal distribution to generate test values
normal_95 = ndtri(0.95)
mean = 0
upper = mean + normal_95
lower = mean - normal_95
obs_mean,obs_var =\
fit_normal_to_confidence_interval(upper,lower,confidence=0.95)
exp_mean = mean
exp_var = 1.0
self.assertFloatEqual(obs_mean,exp_mean)
self.assertFloatEqual(obs_var,exp_var)
#An alternative normal:
normal_99 = ndtri(0.99)
mean = 5.0
upper = mean + normal_99
lower = mean - normal_99
obs_mean,obs_var =\
fit_normal_to_confidence_interval(upper,lower,confidence=0.99)
exp_mean = mean
exp_var = 1.0
self.assertFloatEqual(obs_mean,exp_mean)
self.assertFloatEqual(obs_var,exp_var)
def test_fit_normal_to_confidence_interval(self):
"""fit_normal_to_confidence_interval should return a mean and variance given CI"""
#Lets use a normal distribution to generate test values
normal_95 = ndtri(0.95)
mean = 0
upper = mean + normal_95
lower = mean - normal_95
obs_mean,obs_var =\
fit_normal_to_confidence_interval(upper,lower,confidence=0.95)
exp_mean = mean
exp_var = 1.0
self.assertFloatEqual(obs_mean,exp_mean)
self.assertFloatEqual(obs_var,exp_var)
#An alternative normal:
normal_99 = ndtri(0.99)
mean = 5.0
upper = mean + normal_99
lower = mean - normal_99
obs_mean,obs_var =\
fit_normal_to_confidence_interval(upper,lower,confidence=0.99)
exp_mean = mean
exp_var = 1.0
self.assertFloatEqual(obs_mean,exp_mean)
self.assertFloatEqual(obs_var,exp_var)
def fit_normal_to_confidence_interval(upper,lower,mean=None, confidence = 0.95):
"""Return the mean and variance for a normal distribution given confidence intervals
upper -- upper bound
lower -- lower bound
mean -- mean, if known. If not specified, will be set to be
halfway between upper & lower bounds
confidence -- the confidence for this interval, e.g.
0.95 for the 95% confidence intervals
"""
#Start by calculating Z-scores using the inverse normal distribution,
#starting with the given confidence value
z = ndtri(confidence)
#print "Z:",z
#Now we need to fit a normal distribution given the confidence
#limits
if mean is None:
mean = (upper+lower)/2.0
#print "mean:",mean
#Z-score = deviation from mean/ stdev (equivalently x-mu/sigma)
# Therefore with a little algebra we get stdev = (upper_CI - mean)/Z
estimated_stdev = abs(upper-mean)/z
#print "stdev:",estimated_stdev
variance = estimated_stdev**2 #i.e. sigma^2
#print "var:",variance
return mean,variance
def test_ndtri(self):
"""ndtri should give same result as implementation in cephes"""
exp=[-1.79769313486e+308,
-2.32634787404,
-2.05374891063,
-1.88079360815,
-1.75068607125,
-1.64485362695,
-1.5547735946,
-1.47579102818,
-1.40507156031,
-1.34075503369,
-1.28155156554,
-1.22652812004,
-1.17498679207,
-1.12639112904,
-1.08031934081,
-1.03643338949,
-0.99445788321,
-0.954165253146,
-0.915365087843,
-0.877896295051,
-0.841621233573,
-0.806421247018,
-0.772193214189,
-0.738846849185,
-0.70630256284,
-0.674489750196,
-0.643345405393,
-0.612812991017,
-0.582841507271,
-0.553384719556,
-0.524400512708,
-0.495850347347,
-0.467698799115,
-0.439913165673,
-0.412463129441,
-0.385320466408,
-0.358458793251,
-0.331853346437,
-0.305480788099,
-0.279319034447,
-0.253347103136,
-0.227544976641,
-0.201893479142,
-0.176374164781,
-0.150969215497,
-0.125661346855,
-0.100433720511,
-0.0752698620998,
-0.0501535834647,
-0.0250689082587,
0.0,
0.0250689082587,
0.0501535834647,
0.0752698620998,
0.100433720511,
0.125661346855,
0.150969215497,
0.176374164781,
0.201893479142,
0.227544976641,
0.253347103136,
0.279319034447,
0.305480788099,
0.331853346437,
0.358458793251,
0.385320466408,
0.412463129441,
0.439913165673,
0.467698799115,
0.495850347347,
0.524400512708,
0.553384719556,
0.582841507271,
0.612812991017,
0.643345405393,
0.674489750196,
0.70630256284,
0.738846849185,
0.772193214189,
0.806421247018,
0.841621233573,
0.877896295051,
0.915365087843,
0.954165253146,
0.99445788321,
1.03643338949,
1.08031934081,
1.12639112904,
1.17498679207,
1.22652812004,
1.28155156554,
1.34075503369,
1.40507156031,
1.47579102818,
1.5547735946,
1.64485362695,
1.75068607125,
1.88079360815,
2.05374891063,
2.32634787404,
]
obs = [ndtri(i/100.0) for i in range(100)]
self.assertFloatEqual(obs, exp)
def test_ndtri(self):
"""ndtri should give same result as implementation in cephes"""
exp = [
-1.79769313486e+308,
-2.32634787404,
-2.05374891063,
-1.88079360815,
-1.75068607125,
-1.64485362695,
-1.5547735946,
-1.47579102818,
-1.40507156031,
-1.34075503369,
-1.28155156554,
-1.22652812004,
-1.17498679207,
-1.12639112904,
-1.08031934081,
-1.03643338949,
-0.99445788321,
-0.954165253146,
-0.915365087843,
-0.877896295051,
-0.841621233573,
-0.806421247018,
-0.772193214189,
-0.738846849185,
-0.70630256284,
-0.674489750196,
-0.643345405393,
-0.612812991017,
-0.582841507271,
-0.553384719556,
-0.524400512708,
-0.495850347347,
-0.467698799115,
-0.439913165673,
-0.412463129441,
-0.385320466408,
-0.358458793251,
-0.331853346437,
-0.305480788099,
-0.279319034447,
-0.253347103136,
-0.227544976641,
-0.201893479142,
-0.176374164781,
-0.150969215497,
-0.125661346855,
-0.100433720511,
-0.0752698620998,
-0.0501535834647,
-0.0250689082587,
0.0,
0.0250689082587,
0.0501535834647,
0.0752698620998,
0.100433720511,
0.125661346855,
0.150969215497,
0.176374164781,
0.201893479142,
0.227544976641,
0.253347103136,
0.279319034447,
0.305480788099,
0.331853346437,
0.358458793251,
0.385320466408,
0.412463129441,
0.439913165673,
0.467698799115,
0.495850347347,
0.524400512708,
0.553384719556,
0.582841507271,
0.612812991017,
0.643345405393,
0.674489750196,
0.70630256284,
0.738846849185,
0.772193214189,
0.806421247018,
0.841621233573,
0.877896295051,
0.915365087843,
0.954165253146,
0.99445788321,
1.03643338949,
1.08031934081,
1.12639112904,
1.17498679207,
1.22652812004,
1.28155156554,
1.34075503369,
1.40507156031,
1.47579102818,
1.5547735946,
1.64485362695,
1.75068607125,
1.88079360815,
2.05374891063,
2.32634787404,
]
obs = [ndtri(i / 100.0) for i in range(100)]
self.assertFloatEqual(obs, exp)
