Random number generator of normal (Gaussian) distribution with parameters

a

and

s

. You can obtain any successive random number

x

of the standard normal distribution by the inverse transformation method from the following formula:

where

u

is a random number uniformly distributed over the interval (-1, 1), and

erf

-1

(

u

) is inverse to the error function .

The normal distribution with parameters

a

and

s

is transformed to the random number

y

by scaling and the shift

y = sx+a

.