uniform_to_exponential.R

# How to simulate exponential random variable Y

# Sample sizes
n = 300

lambda = 1  # Choose lambda for exponential distribution

X = runif(n=n, min=0, max=1)    # Sample X from uniform(0, 1)

Y = -1/lambda * log(1-X)        # Compute Y using inverse of CDF for an exponential r.v.

title = paste('n =', toString(n))

hist(Y, probability = TRUE, main=title)           # histogram of random samples Y
rug(Y)                                            # rug plot

curve(dexp(x, rate=lambda), add=TRUE, col='red')  # theoretical density function of y for comparison