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Lowbaer's avatar
Lowbaer
Copper Contributor
May 11, 2024
Solved

Distribution of one number over different categories with specific probabilities per category

Hi all,   I've been trying to create a formula to distribute a given amount of points over multiple different categories with different probabilities for each individual category. So for example 1...
excel
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  • Riny_van_Eekelen's avatar
    Riny_van_Eekelen
    May 12, 2024

    Lowbaer OK, so you want to generate 6 random percentages that add up to 100%.

    In older versions of Excel, use =RAND() in 6 cells and then express each of these as a percentage of their sum. Or if you have a modern Excel version that supports dynamic arrays you could use something like below to spill 6 percentages in one go.

    =LET(
    r, RANDARRAY(1, 6),
    s, SUM(r),
    TRANSPOSE(
        INDEX(r, 1, SEQUENCE(6)) / s
    )
)

     

    The attached file contains both solutions.

Lowbaer's avatar
Lowbaer
Copper Contributor
May 12, 2024
Thats pretty much it! I've taken your formula of the first solution, added a range to the random formula around my desired percentage per category and multiplied the resulting "controlled" random percentages with the total amount of points to be distributed. This does the job, thank you!
rachel's avatar
rachel
Iron Contributor
May 12, 2024
Or you can do it like this: generate a random number between 0 and 100 ten times. For each time, if that number lies in the range of [0, 50], add one point to cat1; if that number lies between 50 and 70, add one point to cat2; if that number is between 70 and 80; add one point to cat3; if the random number lies between 80 and 90, add one point to cat4, if the number lies between 90 and 95, add one point to cat5. if the number lies between 95 to 100, add one point cat6. the excel formula would be =FREQUENCY(RANDARRAY(10,1,0,100,FALSE),{50;70;80;90;95})
  • PeterBartholomew1's avatar
    PeterBartholomew1
    Silver Contributor
    May 13, 2024

    rachel 

    I missed the possibility of using FREQUENCY!

    Lowbaer 

    It turns out that this is somewhat roundabout as a way of generating frequencies!  What I did was to generate a possible result that assigns each of 10 objects to a category with the relevant probabilities

     

    = LET(
    cumulative, SCAN(0, Probability, SUM),
    result, INDEX(Category, XMATCH(RANDARRAY(N),cumulative,1)),
    result
  )

     

    Only then did it sink in that you wanted to know the frequency of each category, not the result itself.

    My solution was to count the occurrences of each category

     

    = LET(
    cumulative, SCAN(0, Probability, SUM),
    result,     INDEX(Category, XMATCH(RANDARRAY(N),cumulative,1)),
    counts,     MAP(Category, LAMBDA(cat, SUM(SIGN(result=cat)))),
    HSTACK(Category, counts)
  )

     

    but to go back to the formula that generates the result and calculate frequencies directly is more efficient

     

    = LET(
    cumulative, SCAN(0, Probability, SUM),
    HSTACK(Category, DROP(FREQUENCY(RANDARRAY(N),cumulative),-1))
  )

     

    Note1:  The 'cumulative' probability gives the array constant in rachel's formula.

    Note2:  DROP is used to remove the count of values exceeding 100%

     

    • rachel's avatar
      rachel
      Iron Contributor
      May 13, 2024
      I was just trying to create an event that happens with 50% probability, 20% probability... etc. Continuous uniform distribution was the first thing that comes to my mind. I even try to google whether RANDARRAY indeed generates N numbers of i.i.d X~U[0, 100].....
  • Lowbaer's avatar
    Lowbaer
    Copper Contributor
    May 12, 2024
    This is an even more elegant solution, thanks!

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