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Math Help - How to 'skew' a uniform distribution

  1. #1
    Hombre
    Guest

    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
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  2. #2
    Newbie
    Joined
    Oct 2012
    From
    S. Africa
    Posts
    12
    Thanks
    1

    Re: How to 'skew' a uniform distribution

    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
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