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From Ted Dunning <>
Subject Re: [Math] Issue 348
Date Sat, 06 Mar 2010 00:33:43 GMT
Here is one.  The goal is to provide an over-dispersed exponential
distribution which is defined as an exponential distribution with a prior
distribution on the lambda parameter.

 * Sample from an exponential distribution whose parameter is distributed
 * to a Gamma distribution.
public class UncertainExponentialDistribution extends
ExponentialDistribution {
    private Gamma prior;

    public UncertainExponentialDistribution(double alpha, double beta) {
        prior = new Gamma(alpha, beta);

    public double getLambda() {

Doing this with an immutable super class is a royal pain in the ass.  Doing
this with setters on lambda isn't sooo bad, but it really obscures the real
point which is that the over-dispersed exponential distribution is *exactly*
an exponential distribution but lambda varies.  The implementation above
says exactly that.

So what about the layer below?  The exponential can be defined as a
specialized Gamma which benefits from the same sort of idiom (yes I know
that this distribution can be implemented as -lambda * log(1-rand()), but we
are talking principles here, not specifics).

public class ExponentialDistribution extends AbstractDistribution {
    private double lambda;

    private Gamma wrapped;

    public ExponentialDistribution() {

    public ExponentialDistribution(double lambda) {
        this.lambda = lambda;
        wrapped = new Gamma(1, 1 / lambda) {
            public double getAlpha() {
                return 1;

            public double getBeta() {
                return 1 / getLambda();

    public double next() {

     * Default implementation of this getter just returns the value we
know.  Sub-classes
     * might over-ride this for special effects.
     * @return
    public double getLambda() {
        return lambda;

Again, we have clarity of expression.  The phrase "gamma distribution with
alpha = 1 and beta = 1/lambda" is just what is in the code here.  You
*could* do this with setters, but at considerable loss of clarity and no
gain in efficiency.

On Fri, Mar 5, 2010 at 3:51 PM, Gilles Sadowski <> wrote:

> Sorry, I don't follow you. Could you give a code example of these
> one-liners?

Ted Dunning, CTO

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