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rrandomdistribution

Sample from a skewed distribution in R

I want to sample numbers from a skewed distribution in R. Let's say I want to sample numbers from a distribution with mode 10 and 95% of values between 5 and 20.

Is there a function in R, similar to rnorm() or runif() that can generate random numbers from such a distribution?

Solution

  • Choosing a log normal distribution with μ = 2.415195 and σ = 0.3355733 will give a distrubution with (approximately) your requirements.

    mu <- 2.415195
sigma <- 0.3355733

N <- 10000000
nums <- rlnorm(N, mu, sigma)

    Approximately 95% of values are between 5 and 20.

    sum(5 < nums & nums < 20) / N
#> [1] 0.9500141

    Mode is 10

    ggplot(tibble(x = nums), aes(x)) +
  geom_density() +
  geom_vline(xintercept = 10, color = "red") +
  geom_vline(xintercept = c(5, 20), color = "blue")

    distribution

    I got these parameters using optimize.

    From any σ, we can calculate what μ gives us a mode of 10 because the mode is: mode

    So we want to find what σ gets us closest to 95% of values between 5 and 20. This can be calculated from the difference between cdf(20) and cdf(5). The CDF for the log normal distribution is: cdf. (plnorm in R).

    f <- function(sigma) {
  mu <- log(10) + sigma^2
  
  abs(plnorm(20, mu, sigma) - plnorm(5, mu, sigma) - 0.95)
}

optimize(f, lower = 0, upper = 1)
#> $minimum
#> [1] 0.3355733
#> 
#> $objective
#> [1] 1.160349e-05