Thread: How to 'skew' a uniform distribution

Hi,

I am trying to figure out the following:

Let's say I have a random (unsorted) set of 100 integers. Each integer comes from the domain 1 to 4 ({1,2,3,4}) and all integers are uniformly distributed, so:

1: 25 times
2: 25 times
3: 25 times
4: 25 times

I'm looking for a way to:
a) 'skew' this set of integers AND
b) the integer with the highest frequency must appear at least 75 times.

e.g. If we skew the a distribution where the value of '3' is the most frequent.

1: 6 times
2: 8 times
3: 75 times
4: 11 times

My questions are:
1) I am looking for a function to skew the uniform distribution and to make it non-uniform. And (yes, I want it all...;-))
2) I am looking for a function to reverse this operation using the non-uniform distribution as input and transform it back into the original uniform distribution.

I would like to know whether this is possible yes or not. Please keep it simple, I consider myself not a math expert.

Thanks for any help/replies in advance.

Kind regards

If you are fitting a quadratic model:

f(x) = ax^2+bx+c

f(1)=0.06
f(2)=0.08
f(3)=0.75
f(4)=0.11
f(x) = ax^2+bx+c

solve for a,b,c
1= Σ(ax^2+bx+c)
a+b+c=0.06
4a+2b+c=0.08