<Ul> <Li> Marsaglia polar method is a modification of the Box--Muller method algorithm, which does not require computation of functions sin () and cos (). In this method U and V are drawn from the uniform (− 1, 1) distribution, and then S = U + V is computed . If S is greater or equal to one then the method starts over, otherwise two quantities </Li> </Ul> <Li> Marsaglia polar method is a modification of the Box--Muller method algorithm, which does not require computation of functions sin () and cos (). In this method U and V are drawn from the uniform (− 1, 1) distribution, and then S = U + V is computed . If S is greater or equal to one then the method starts over, otherwise two quantities </Li> <Dl> <Dd> <Dl> <Dd> X = U − 2 ln ⁡ S S, Y = V − 2 ln ⁡ S S (\ displaystyle X = U (\ sqrt (\ frac (- 2 \ ln S) (S))), \ qquad Y = V (\ sqrt (\ frac (- 2 \ ln S) (S)))) </Dd> </Dl> </Dd> <Dd> are returned . Again, X and Y will be independent and standard normally distributed . </Dd> </Dl> <Dd> <Dl> <Dd> X = U − 2 ln ⁡ S S, Y = V − 2 ln ⁡ S S (\ displaystyle X = U (\ sqrt (\ frac (- 2 \ ln S) (S))), \ qquad Y = V (\ sqrt (\ frac (- 2 \ ln S) (S)))) </Dd> </Dl> </Dd>

Third order central moment of the normal distribution is