def _eval_apply_evalf(self, arg):
arg = arg.evalf()
if isinstance(arg, Basic.Number):
# Temporary hack
from sympy.core.numbers import Real
from sympy.numerics import evalf
from sympy.numerics.functions2 import erf
e = erf(evalf(arg))
return Real(str(e))
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.
Examples usage:
# One standard deviation
>>> N = Normal(0, 1)
>>> N.confidence(0.68)
(-0.994457883209753, 0.994457883209753)
>>> N.probability(*_).evalf()
0.68
# Two standard deviations
>>> N = Normal(0, 1)
>>> N.confidence(0.95)
(-1.95996398454005, 1.95996398454005)
>>> N.probability(*_).evalf()
0.95
"""
if p == 1:
return (-oo, oo)
assert p <= 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.numerics import Float, secant, evalf
from sympy.numerics.functions2 import erf
p = evalf(p)
# calculate y = ierf(p) by solving erf(y) - p = 0
y = secant(lambda y: erf(y) - p, 0)
t = Real(str(evalf(s.sigma) * Float(2)**0.5 * y))
mu = s.mu.evalf()
return (mu-t, mu+t)