Java Generator for Poisson and Uniform Distributions?

Question

From what I understand, the standard generator is for the Normal Distribution. I have to generate random numbers according to the Normal, Uniform and Poisson Distributions,

Answer 1

Let me preface all this by the fact that none of this is truly random, I am talking about pseudo random number generators.

Let me also say that I have never had to do this for production quality code. I have done this for a hw assignment though, in Python. I simulated Poisson random variables.

The way that I did it made use of the following facts:

1. A Poisson random variable is a sum of exponential random variables.
2. We can use the inverse transform method to generate exponential random variables. http://en.wikipedia.org/wiki/Inverse_transform_sampling.

In particular, you can use the fact that: if X₁, ..., X_n are independent standard exponential random variables, then Z = min(k : X₁ + ... + X_k < λ) - 1 is Poisson(λ).

So, with that, I wrote the following code in python to generate Poisson values:

class Poisson:
    """Generate Poisson(lambda) values by using exponential
    random variables."""

    def __init__(self, lam):
        self.__lam = lam

    def nextPoisson(self):
        sum = 0
        n = -1
        while sum < self.__lam:
            n += 1
            sum -= math.log(random.random())
        return n

Example usage of the class is:

# Generates a random value that is Poisson(lambda = 5) distributed
poisson = Poisson(5)
poisson_value = poisson.nextPoisson

I posted this here because it is good to know that these kinds of relationships exist, and this inverse transform method gives you a general way to deal with generating random values following a particular continuous distribution.