InverseCDF works fine with the normal distribution quite far out on the right tail, but eventually I am getting an $\infty$ error. Thus
N[InverseCDF[NormalDistribution[], 1 - 9*10^-15]]
gives
7.66416
but
N[InverseCDF[NormalDistribution[], 1 - 9.1*10^-15]]
gives
∞
How can I avoid getting the infinity error?
A series expansion helps to stabilize the calculation:
a[y_] = Assuming[0 < y < 1,
FullSimplify[Normal[Series[InverseCDF[NormalDistribution[], 1-y], {y, 0, 1}]]]]
(* Sqrt[-2*Log[y] - Log[-2*π*Log[2*π*y^2]]] *)
Evaluation is now very stable even for small values of $y$:
a[9.1*10^-15]
(* 7.66047 *)
a[3.7*10^-81]
(* 19.0435 *)
N[InverseCDF[NormalDistribution[], 1 - 91*10^-16]]gives 7.66275. And don't be surprised if this question is closed because this is a common issue. See reference.wolfram.com/language/tutorial/Numbers.html#21155 and mathematica.stackexchange.com/questions/118797/…. $\endgroup$