> > Well, the problem is this: If I need to create some custom discrete
> > distribution that doesn't take on integer values, what interface should I
> > implement? With your model I have no choice but use the
> > ContinuousDistribution interface even though the distribution *isn't*
> > continuous. Does that make sense?
>
> Can you provide a practical example of this? IIUC, what you are really
> arguing for is changing the int's in the DiscreteDistribution interface to
> doubles. This has the advantage of greater generality but makes it
> slightly less convenient for implementors of the most common discrete
> distributions, where the values are integers.
Well, changing the int's in the DiscreteDistribution interface to doubles is
kind of a workaround, but I don't think it will settle the issue for good,
see below.
As for examples, you can take *any* mixed distribution as an example of what I
mean. Consider a random variable X with domain D that can be partitioned
into subsets A and B such that
1. A is a countable set and 0 < P(X is in A) < 1
2. P(X = x) = 0 for all x in B
How would the distribution for such a random variable be represented in
your framework?
As a simple example of this, consider a random variable with the density
f(x) = 0.5 for x=0
f(x) = 0.5 for 1<x<2
How does this distribution fit into your framework? Sure, you could have
it implement the ContinuousDistribution interface but it *isn't* a
continuous distribution (in the sense that it doesn't conform to the
definition of a continuous distribution in probability theory) - and
then it shouldn't implement an interface called ContinuousDistribution.
Recall: A random variable is continuous if its distribution function P(X <= x)
can be expressed as the Riemann-integral of some integrable function
f: R -> [0, infinity)
The basic problem is that you have an implicit assumption in your
framework that each and every probability distribution can be classified
as being either discrete or continuous . That is simply not true.
Discrete and continuous distributions are really only special cases of
a broader concept. Aside from that you also have the problem of how to
handle the case of a discrete distribution that doesn't take on integer
values.
Note: There are also distributions that are neither discrete, continuous or a
mixture of the two. For example, there are numerous distributions based upon
the Cantor ternary sets.
The bottom line is that you *cannot* do without a generic
ProbabilityDistribution interface.
This interface should expose a method that exists for all and completely
determines a particular probability distribution, such as the
distribution function P(X <= x).
As an easy solution, you could define it as
public interface ProbabilityDistribution {
��������public double distributionFunction(double x);
}
and have ContinuousDistribution and DiscreteDistribution extend it.
This should work ok (though the name DiscreteDistribution is misleading)
but if you want a completely generic and typesafe definition you should
go for something like
public interface ProbabilityDistribution {
��������public Probability distributionFunction(Number x);
}
where Number is the standard java.lang.Number and Probability is a new
class that would need to be defined. Since probability measure is the
fundamental concept in probability theory, having a Probability class is
probably a good idea anyway. It could look something like this
public final class Probability implements Serializable {
� � public static final Probability PROPABILITY_ONE = new
Probability(1);
� � public static final Probability PROPABILITY_ZERO = new
Probability(0);
� � private double value;
� � public Probability(double v) throws IllegalArgumentException {
� � � � if (v < 0 || v > 1) {
� � � � � � throw new IllegalArgumentException("Illegal probability
value.");
� � � � }
� � � � this.value = v;
� � }
� � public double value() {
� � � � return value;
� � }
}
(A custom equals method should also be provided of course.)
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