def confidence(s, p):
"""Return a symmetric (p*100)% confidence interval. For example,
p=0.95 gives a 95% confidence interval. Currently this function
only handles numerical values except in the trivial case p=1.
For example, one standard deviation:
>>> from sympy.statistics import Normal
>>> N = Normal(0, 1)
>>> N.confidence(0.68)
(-0.994457883209753, 0.994457883209753)
>>> N.probability(*_).evalf()
0.680000000000000
Two standard deviations:
>>> N = Normal(0, 1)
>>> N.confidence(0.95)
(-1.95996398454005, 1.95996398454005)
>>> N.probability(*_).evalf()
0.950000000000000
"""
if p == 1:
return (-oo, oo)
if p > 1:
raise ValueError("p cannot be greater than 1")
# In terms of n*sigma, we have n = sqrt(2)*ierf(p). The inverse
# error function is not yet implemented in SymPy but can easily be
# computed numerically
from sympy.mpmath import mpf, erfinv
# calculate y = ierf(p) by solving erf(y) - p = 0
y = erfinv(mpf(p))
t = Float(str(mpf(float(s.sigma)) * mpf(2)**0.5 * y))
mu = s.mu.evalf()
return (mu - t, mu + t)
def confidence(s, p):
"""Return a symmetric (p*100)% confidence interval. For example,
p=0.95 gives a 95% confidence interval. Currently this function
only handles numerical values except in the trivial case p=1.
For example, one standard deviation:
>>> from sympy.statistics import Normal
>>> N = Normal(0, 1)
>>> N.confidence(0.68)
(-0.994457883209753, 0.994457883209753)
>>> N.probability(*_).evalf()
0.680000000000000
Two standard deviations:
>>> N = Normal(0, 1)
>>> N.confidence(0.95)
(-1.95996398454005, 1.95996398454005)
>>> N.probability(*_).evalf()
0.950000000000000
"""
if p == 1:
return (-oo, oo)
if p > 1:
raise ValueError("p cannot be greater than 1")
# In terms of n*sigma, we have n = sqrt(2)*ierf(p). The inverse
# error function is not yet implemented in SymPy but can easily be
# computed numerically
from sympy.mpmath import mpf, erfinv
# calculate y = ierf(p) by solving erf(y) - p = 0
y = erfinv(mpf(p))
t = Float(str(mpf(float(s.sigma)) * mpf(2)**0.5 * y))
mu = s.mu.evalf()
return (mu - t, mu + t)
