Hello.
Le dim. 1 août 2021 à 16:45, Alex Herbert <alex.d.herb...@gmail.com> a écrit :
>
> 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
Do you think that the API defined in the
"commons-statistics-distribution"
module is suitable for implementing this concept:
https://en.wikipedia.org/wiki/Distribution_(mathematics)
?
> 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
+1
Thanks,
Gilles
> 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
---------------------------------------------------------------------
To unsubscribe, e-mail: dev-unsubscr...@commons.apache.org
For additional commands, e-mail: dev-h...@commons.apache.org
