TITLE: How do I convert a uniform value in [0,1) to a standard normal (Gaussian) distribution value?
QUESTION [13 upvotes]: I have uniform value in [0,1). I'd like to transform it into a standard normal distribution value, in a deterministic fashion.
What I'm confused about with the Box-Muller transform is that it takes two uniform values in [0, 1), and transform them into two normal random values.
However, I only have one uniform value. How do I apply Box-Muller over a single value?

REPLY [2 votes]: The best way to obtain the inversion from U[0, 1] to Normal distribution is by using an algorithm presented in a famous short paper of Moro (1995). Moro presented a hybrid algorithm: he uses the Beasley & Springer algorithm for the central part of the Normal distribution and another algorithm for the tails of the distribution.
He modeled the distribution tails using truncated Chebyschev series.....
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http://marcoagd.usuarios.rdc.puc-rio.br/quasi_mc.html