Creating a distribution with specific mean and variance in FORTRAN 90

[sue132]

Hi,

I'm trying to create a normal distribution with mean 0.5 and variance 0.05. I tried it initially with MATLAB, for which I used

newdist=0.5+(randn(1,1000)*sqrt(0.05));

Could you please help me in doing this in FORTRAN 90? Would generating a sequence using RANDOM_NUMBER and using the above equation give me similar results?

Thank you.

(P.S. : The LINUX OS on my system needs to be replaced, and I'm writing some more code before I can run them on another system. It would be great to have your help in the meanwhile, so I could check everything together. Thanks again)

 

[DrClaude]

You can't do it directly with random_number, which has a uniform distribution. There are different ways to produce a normal distribution from a uniform distribution, such as the Box-Muller transform.

 

[I like Serena]

Hi sue132!

http://www.ohio.edu/people/just/Escalate/source/random.ccsome C source code for nrandom that generates normally distributed random numbers (based on the Box-muller transform).

The algorithm is easy to port to any computer language.
It comes from Numerical Recipes in C, for which there is also a FORTRAN version.

 

[sue132]

Thank you for the replies

 

[LudusRex]

Hi,

Creating a normal distribution with specific mean and variance in FORTRAN 90 can be achieved by using the RANDOM_NUMBER subroutine and the formula for calculating a normal distribution. Here is an example code that you can use:

PROGRAM normal_dist
IMPLICIT NONE

! Define variables
INTEGER :: i, n = 1000
REAL :: mean = 0.5, variance = 0.05
REAL :: x(n), u(n), v(n)

! Generate n random numbers between 0 and 1
CALL RANDOM_NUMBER(u)

! Calculate the standard normal distribution using Box-Muller transform
DO i = 1, n, 2
v(i) = SQRT(-2.0 * LOG(u(i))) * COS(2.0 * PI * u(i + 1))
v(i + 1) = SQRT(-2.0 * LOG(u(i))) * SIN(2.0 * PI * u(i + 1))
END DO

! Calculate the desired normal distribution
x = mean + SQRT(variance) * v

! Print the results
WRITE(*,*) "Generated normal distribution with mean = ", mean, " and variance = ", variance
WRITE(*,*) "First 10 values: ", x(1:10)

END PROGRAM normal_dist

This code uses the Box-Muller transform to generate a standard normal distribution and then scales it according to the desired mean and variance. You can change the values of mean and variance to get different distributions.
I hope this helps. Happy coding!