- Many continuous distributions don't have a closed-form
inverse function. Strictly speaking, the inverse transform method
discussed earlier cannot be applied.
- If we are willing to accept numeric solution, inverse
functions can be found. Here we have an example for normal
distribution.
- One of the inverse cdf of the standard normal distribution
was proposed by Schmeiser:

for which matches the true normal distribution with one digit after decimal point. See Table 9.6 on page 335.

Meng Xiannong 2002-10-18