Create a data frame with three columns and each row with a constant sum

Question

I want to create a large data frame (100,000 rows and 3 columns) that has three columns (A, B and C).

This data frame satisfies two conditions:

• in each row A+B+C=1;
• all A have a triangular distribution (min = 0.2, mod = 0.3, max = 0.4), all B have a triangular distribution (min = 0.3, mod = 0.4, max = 0.5), and all C have a triangular distribution (min = 0.1, mod = 0.3, max = 0.5).

I could not figure out how to create such a dataset.

Thanks so much for your suggestions in advance.

Songchao

Answer 1

N <- 100000

library(triangle)

A <- rtriangle(N, 0.2, 0.4, 0.3)
B <- rtriangle(N, 0.3, 0.5, 0.4)
C <- 1 - A - B

d = data.frame(A, B, C)
summary(d)

changed later

nr <- 100000

u1 <- runif(nr)
u2 <- runif(nr)
u3 <- (2 - u1 - u2) / 2

U <- cbind(u1, u2, u3)

# shuffle, because I am not sure about the tails of u3
for (i in (1:nrow(U))) {
  U[i, ] <- U[i, sample(1:3)]
}

t1 <- qtriangle(U[, 1], 0.2, 0.4, 0.3)
t2 <- qtriangle(U[, 2], 0.3, 0.5, 0.4)
t3 <- qtriangle(U[, 3], 0.1, 0.5, 0.3)

d <- cbind(t1, t2, t3)
summary(d)
cor(d)

Answer 2

I am not sure if this works, as I am not sure if the conversion kills the distribution, but try the following:

install.packages("triangle") #if not already present
library(triangle)

a <- rtriangle(10, a = .2, b = .4)
b <- rtriangle(10, a = .3, b = .5)
c <- rtriangle(10, a = .1, b = .5)

m <- cbind(a, b, c)
test <- sweep(m, 1, rowSums(m), FUN = "/") #divide all rows by their rowSums

> test
              a         b         c
 [1,] 0.3237202 0.4034106 0.2728692
 [2,] 0.2419613 0.3821729 0.3758658
 [3,] 0.2476927 0.3721925 0.3801149
 [4,] 0.2983462 0.4254064 0.2762474
 [5,] 0.3427140 0.4830743 0.1742117
 [6,] 0.2456610 0.3306648 0.4236742
 [7,] 0.3189454 0.4148087 0.2662459
 [8,] 0.3400111 0.3770924 0.2828965
 [9,] 0.3142197 0.3807667 0.3050136
[10,] 0.3221066 0.4222530 0.2556405
> rowSums(test)
 [1] 1 1 1 1 1 1 1 1 1 1