Produce m uniformly distributed numbers that add up to 1 in R

Question

Given m , how can we generate m uniformly distributed numbers that sum with 1 such that A1 > A2 > ... > Am ?

For example, if m=4 , then we should have:

 a <- c(0.4, 0.3, 0.2, 0.1) abs(diff(a)) #[1] 0.1 0.1 0.1 sum(a) #[1] 1 

Or for m=5 :

 b <- c(0.30, 0.25, 0.20, 0.15, 0.10) abs(diff(b)) #[1] 0.05 0.05 0.05 0.05 sum(b) #[1] 

Answer 1

If you want to adjust the space or the starting point, you can use the formula to calculate the space based on the starting point or the starting point based on space:

Scenario 1: custom starting point:

 m = 5; s = 0.9 seq(from = s, by = -(m*s - 1) * 2/((m - 1) * m), length.out = m) #[1] 0.90 0.55 0.20 -0.15 -0.50 sum(seq(from = s, by = -(m*s - 1) * 2/((m - 1) * m), length.out = m)) #[1] 1 

Scenario 2: Adjustable space:

 m = 5; d = 0.2 seq(from = 1/m + ((m - 1) * d/2), by = -d, length.out = m) # [1] 0.6 0.4 0.2 0.0 -0.2 sum(seq(from = 1/m + ((m - 1) * d/2), by = -d, length.out = m)) # [1] 1 

Answer 2

What about:

 rev(seq_len(m)/sum(seq_len(m))) a <- rev(seq_len(4)/sum(seq_len(4))) ##[1] 0.4 0.3 0.2 0.1 abs(diff(a)) ##[1] 0.1 0.1 0.1 sum(a) ##[1] 1 b <- rev(seq_len(5)/sum(seq_len(5))) ##[1] 0.33333333 0.26666667 0.20000000 0.13333333 0.06666667 abs(diff(b)) ##[1] 0.06666667 0.06666667 0.06666667 0.06666667 sum(b) ##[1] 1