Simulate a data frame with different sequence per column

Question

I would like to simulate in R a data frame with 4 columns with the above conditions:

1. Each row is summing up to 1

2. The first element of column 1 starts with being closer to 1, say 0.9, but gradually decreases per row.

3. The elements of the other 3 columns start low, say something between 0.02 - 0.05, but gradually increase with each row.

4. I would like the last row of the data frame being c(0.25, 0.25, 0.25, 0.25).

Can you help me with creating something like that ? Thank you in advance!

Answer 1

# State the number of rows you want to create
rows <- 1000

# Create 4 randomly generated columns, the first ranging [.25, 1], the others [0, .25] and add .25 as the last row
x1<-c(runif(rows-1,.25,1), .25)
x2<-c(runif(rows-1,0,.25), .25)
x3<-c(runif(rows-1,0,.25), .25)
x4<-c(runif(rows-1,0,.25), .25)

library(dplyr)
# Combine the columns into a single table
df <- data.frame(x1, x2, x3, x4)

df %>% 
  # Sort each column individually (meaning the sorting of 1 column doesn't affect another)
  mutate(x1 = sort(x1, decreasing = T)) %>%
  mutate(across(x2:x4, ~sort(.x))) %>%
  # Transpose the table so you can sort the rows
  t() %>%
  as_tibble() %>%
  mutate_all(.funs = ~sort(., decreasing = T)) %>%
  t() %>%
  as_tibble() %>%
  # Scale the table you have so the sum of each row equals to 1
  mutate_all(.funs = ~ ./rowSums(across(everything())))