Generate probability vectors

General
1

I am interested in generating a list of n random numbers that add up to 1 and are all non-negative, that is, a probability vector. As an example, I have tried the following simple approach:

n=10
v=rbeta(n,shape1=2,shape2=5)
v/sum(v)

However, I don't think this approach is correct, given that the number of degrees of freedom is n-1, instead of n.

Does anyone know how can this be done more correctly?

Thanks in advance for any help!

2

The first thing that came to my mind was the dirichlet distribution which is a multivariate beta distribution. This package has a function rdirichlet to randomly generate the vectors.

2 Likes
3

Oh and the dirichlet generation is equivalent to doing what you did - using the beta and dividing by the sum of independent beta draws. It will have n-1 degrees of freedom because of the constraint it sums to 1.

1 Like
4

Thanks for the answer! It was really helpful. I didn't know about the Dirichlet distribution, pretty interesting

5

How about this:

x <- seq( from = 1, to = 100, by = 1)
s <- sample(x, 5)
s
sum_s <- sum(s)
s <- s/sum_s
s

6

Thanks for the answer. I guess the method you propose is equivalent, just employing a uniform distribution instead of beta distributions

7

I was surprised to see the beta distribution here. You didn't mention anything about your data to suggest anything about the shape of the distribution.

8

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