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copied!<p>Let me preface all this by the fact that none of this is truly random, I am talking about pseudo random number generators.</p> <p>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.</p> <p>The way that I did it made use of the following facts: </p> <ol> <li>A Poisson random variable is a sum of exponential random variables.</li> <li>We can use the inverse transform method to generate exponential random variables. <a href="http://en.wikipedia.org/wiki/Inverse_transform_sampling" rel="nofollow noreferrer">http://en.wikipedia.org/wiki/Inverse_transform_sampling</a>.</li> </ol> <p>In particular, you can use the fact that: if X<sub>1</sub>, ..., X<sub>n</sub> are independent <em>standard</em> exponential random variables, then Z = min(k : X<sub>1</sub> + ... + X<sub>k</sub> < λ) - 1 is Poisson(λ).</p> <p>So, with that, I wrote the following code in python to generate Poisson values:</p> <pre><code>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 </code></pre> <p>Example usage of the class is:</p> <pre><code># Generates a random value that is Poisson(lambda = 5) distributed poisson = Poisson(5) poisson_value = poisson.nextPoisson </code></pre> <p>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.</p>

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