[Solved] How to create 4 random defined percentages that sum 1

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Introduction

If you are looking for a way to create four random defined percentages that sum to 1, then you have come to the right place. In this article, we will provide a step-by-step guide on how to generate four random defined percentages that sum to 1. We will also discuss the importance of using random defined percentages and the various methods you can use to generate them. By the end of this article, you should have a better understanding of how to create four random defined percentages that sum to 1.

Solution

One way to create 4 random defined percentages that sum 1 is to generate 4 random numbers between 0 and 1, then divide each number by the sum of all 4 numbers.

For example, if the 4 random numbers are 0.2, 0.3, 0.4, and 0.1, the 4 percentages would be 0.2/1 = 0.2, 0.3/1 = 0.3, 0.4/1 = 0.4, and 0.1/1 = 0.1, which all sum to 1.


Let

ll <- c(0.2, 0.2, 0.15, 0.15)
ul <- c(0.5, 0.5, 0.4, 0.3)

where ll and ul correspond to lower and upper limits for each of the random variables. Next,

x <- runif(length(ll), 0, ul - ll)

is a vector of uniform random draws from intervals [0,0.3], [0,0.3], [0,0.25], and [0,0.15]. The reason for this is that our final vector is

if(sum(x) > 1 - sum(ll)) {
  ll + x / sum(x) * (1 - sum(ll))
} else {
  ll + x + (ul - ll - x) / sum(ul - ll - x) * (1 - sum(x) - sum(ll))
}
# [1] 0.3112532 0.2927185 0.2347163 0.1613119

So, if sum(x) > 1 - sum(ll), this means that x is too large. In that case we renormalize it by making it smaller. In this way all the constraints are satisfied. Otherwise, x is too small. In that case we are going to add a portion of ul - ll - x. Now the key is that necessarily

sum(ul - ll - x) > (1 - sum(x) - sum(ll))

which means that ul - ll - x doesn’t get increased and, hence, again all the restrictions are satisfied.

Kernel densities of the respective elements are as follows

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solved How to create 4 random defined percentages that sum 1


Creating four random defined percentages that sum to 1 can be a tricky task. However, with a few simple steps, you can easily generate four random percentages that add up to 1. Here’s how:

  1. Generate four random numbers between 0 and 1. Make sure that the sum of these four numbers is less than 1.
  2. Divide each of the four random numbers by the sum of all four numbers.
  3. Multiply each of the four numbers by 100 to get the percentages.
  4. Add the four percentages together to make sure they sum to 1.

By following these steps, you can easily generate four random defined percentages that sum to 1. This can be a useful tool for creating random distributions or for other statistical purposes.