Polar Method

Polar Method

to

simulate normal RV from uniform RV

JavaScript has only provided a uniform random variable Math.random() and a normal random number is sometimes a necessary one to have.There is a polar method to simulate normal RV (random variables) from uniform RV in "A First Course of Probability" by Sheldon Ross (pp. 464, 6ed):

Generate random numbers $U_1$ and $U_2$ .
Set $V_1=2U_1-1,V_2=2U_2-1,S=V^2_1+V^2_2$ ,
If $S>1$ , return step 1,
Return the independent unit normals $X=\sqrt{\frac{-2\log{S}}{S}}V_1,Y=\sqrt{\frac{-2\log{S}}{S}}V_2$ .

Here is the (almost) equivalent code in JavaScript:

Number of normals N = 619x
(HTML5 canvas support required)