Generating random poisson numbers

Question

I was writing a function (without using the random.poisson function)that generates a random number from a poisson distribution with lambda a.

When running the function with different parameters, I always get 0. I guess it is the algorithm problem but don't know where is wrong.

Here is my code.

#takes a as lambda (mean)
def random_poisson(a):
    x = 0
    p = 1
    while p >= math.exp(a):
        i = random.random()
        p = p * i
        x += 1

    return x

Trying out different lambda values:

print(random_poisson(3))
print(random_poisson(5))
print(random_poisson(math.log(5)))

The output:

0
0
0

Thanks so much!

Answer 1

For any positive a, math.exp(a) is greater than 1, but p is 1. The loop condition is never true, the loop is never executed, and your function returns the initial value of x.