模拟一个变量的最佳方法是什么，该变量采用 integer 个值，范围从 0 到 40（在 R 中）？ 统计新手

Question

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I am sorry if this question is confusing, but I am stats newbie.. I am trying to simulate a composite variable which takes values ranging from 0 to 40. The composite variable is made of the sum of 8 questions which could take values between 0 and 5. I am aware that I cannot use rnorm , since it will also give me negative values, and the original data is right skewed. I have the probabilities for each score (o to 5) occurring for each of the compositor variables, so I have considered generating each of them separately using the sample function, and then summing them to create my sum variable. However, I am afraid that they probably would be correlated, and I haven't been able to find a way to simulate them simultaneously while also accounting for correlation. Essentially, to make it easier to imagine, the paper contrasts the use of 2 languages in different scenarios, so those same questions are asked twice to each participant for each language. Therefore, the variables might also be correlated between conditions. Is there a way to deal with that, or would it be best to simulate the total score variable directly? From what I understand, although I am not sure if I am correct, I could use the rpois function to do this? Or another solution I could thin of is simulate the data using rnorm , and then square it to make a right skew? Any opinion would be very useful!!! Thank you in advance!!

I have tried using rpois and simulating each compositor variable separately.

Answer 1

Easy enough with the the base R sample function using the probability parameter. Example:

# first generate dummy probabilities
x <- runif(41) #41 possible outcomes 0 to 40
probs <- x / sum(x) # normalize the probability vector to 1
samples <- sample(0:40, 1000, replace = TRUE, prob = probs) # generate 1000 prob weighted realizations