Gaussian distribution question (bell curve creation)

I am struggling with the problem for long

I have a total number of units to be produced say 2000 for product A and production is to be done in one year from Jan-Dec 2013

I want to create a bell-curve that would bi distributed from Jan-Dec. I was think if there is a method that would generate distribution of numbers for every month total being 2000 units and distribution represents a bell curve

please help

thank you in advance

Re: Gaussian distribution question (bell curve creation)

Where is the bell-curve? Do you want a low production in Jan+Dec and a higher production in between? That would fit to your description, but I doubt that you plan to do this.

Do you want roughly the same production in all months, where the production in individual months has a gaussian probability distribution? In this case, it is not trivial (but possible) to require a total production of 2000.

Re: Gaussian distribution question (bell curve creation)

yes I was looking to get lower values on near starting and ends and higher values in between. in simple way we can say to generate between 0 to 10 in five intervals such that total is 10 such as 1,2,4,2,1. Now if it was a one time case then I can do it manually, but I am trying to incorporate an algorithm in a program that would do it pretty often.

Please see if u can provide some guidance. thank you

Re: Gaussian distribution question (bell curve creation)

Let $\displaystyle f(x)=exp(-\frac{(x-x_0)^2}{2\sigma^2})$ be the gaussian distribution without normalisation constant. x is in months or whatever timestep, x_{0} is the point of maximum production (probably close to the middle of your time interval), and $\displaystyle \sigma$ is a parameter for the width of the distribution. Define x_{0} and $\displaystyle \sigma$, evaluate this function for all time steps, determine the sum S. To get a total production of P, multiply your function (and therefore all production values) with P/S.