The ContinuousDistribution interface has the method:
/**
* For a random variable {@code X} whose values are distributed according
* to this distribution, this method returns {@code P(X = x)}.
* In other words, this method represents the probability mass function
* (PMF) for the distribution.
*
* @param x Point at which the PMF is evaluated.
* @return the value of the probability mass function at point {@code x}.
*/
default double probability(double x) {
return 0;
}
This is not overridden by any distribution. The javadoc is a direct copy
from the DiscreteDistribution interface where the PMF has relevance. All
the continuous distributions provide implementations for the related
density method:
/**
* Returns the probability density function (PDF) of this distribution
* evaluated at the specified point {@code x}.
* In general, the PDF is the derivative of the {@link
#cumulativeProbability(double) CDF}.
* If the derivative does not exist at {@code x}, then an appropriate
* replacement should be returned, e.g. {@code Double.POSITIVE_INFINITY},
* {@code Double.NaN}, or the limit inferior or limit superior of the
* difference quotient.
*
* @param x Point at which the PDF is evaluated.
* @return the value of the probability density function at {@code x}.
*/
double density(double x);
It appears odd that the ContinuousDistribution has a probability(x) method
which returns 0 for all implementations, i.e. why have this method? It
could be implemented for the ConstantContinuousDistribution. At least in
this case for a constant value it should return 1 when x is the value of
the distribution.
I have had no luck finding another library that implements this
distribution (e.g. R, matlab, python) and I do not know a use case other
than to implement a Dirac delta function [1]. In this case it is useful to
have the density return 1 such that multiplication by the density is a
linear functional that maps every function to its value at zero:
f(x) * delta(x) = f(0) for x=0, zero otherwise
In other libraries for continuous functions they implement only the
probability density function (PDF) and the cumulative distribution function
(CDF) for both continuous and discrete distributions. There is no
additional probability function.
Thus the method has no use in the current library. Here are two options:
1. Remove the method
2. Implement the method in the ConstantContinuousDistribution to return 1
when the value equals the constant value. It currently does this for the
density function but probability(x) will return zero for all values so it a
bug. This behaviour was ported from Commons Math 3. I find no continuous
distributions that override the probability method there either.
Alex
[1] https://en.wikipedia.org/wiki/Dirac_delta_function
