从定义范围 [min, max] 的泊松分布生成随机数

Question

I would like to draw 100 random numbers from a Poisson distribution with a mean of 0.5, ranging from 0 to 10.

Using the rpois(n = 100, lambda = 0.50) function, I can obtain the random numbers from the Poisson distribution, but I am unable to specify the min/max values.

Any way of doing this in R?

A bit more context: In a dataset, my dependent variable has the properties mentioned above (mean, min, max values), and I would like to estimate some models with simulated data for my dependent variable.

Edit: My dependent variable (for which I want to simulate the random numbers in addition to the observed values) is neither truncated nor censored. However, I should note that its standard deviation is 1, ie, the variance is not equal to the mean of 0.5.

Thanks!

Answer 1

You have limited number of items to sample, just make probabilities to follow Poisson and sample

Along the lines

l <- 0.5

x <- c(0,1,2,3,4,5,6,7,8,9,10)

p <- rep(0, length(x)) # probabilities

s <- 0.0
for (k in x) {
    p[k+1] = l**k * exp(-l) / gamma(k+1)
    s <- s + p[k+1]
}

p = p / s # normalization

print(sample(x, 1, replace=TRUE, prob=p))
print(sample(x, 1, replace=TRUE, prob=p))
print(sample(x, 1, replace=TRUE, prob=p))
print(sample(x, 1, replace=TRUE, prob=p))
print(sample(x, 1, replace=TRUE, prob=p))
print(sample(x, 1, replace=TRUE, prob=p))
print(sample(x, 1, replace=TRUE, prob=p))