diff --git a/src/site/resources/images/userguide/real_distribution_examples.png b/src/site/resources/images/userguide/real_distribution_examples.png deleted file mode 100644 index c7dac7786..000000000 Binary files a/src/site/resources/images/userguide/real_distribution_examples.png and /dev/null differ diff --git a/src/site/xdoc/userguide/distribution.xml b/src/site/xdoc/userguide/distribution.xml index 6fa61f8bf..74a3e3db2 100644 --- a/src/site/xdoc/userguide/distribution.xml +++ b/src/site/xdoc/userguide/distribution.xml @@ -16,7 +16,7 @@ See the License for the specific language governing permissions and limitations under the License. --> - + @@ -26,92 +26,38 @@

- The distributions package provides a framework and implementations for some commonly used - probability distributions. Continuous univariate distributions are represented by implementations of - the RealDistribution - interface. Discrete distributions implement - IntegerDistribution - (values must be mapped to integers) and there is an - EnumeratedDistribution - class representing discrete distributions with a finite, enumerated set of values. Finally, multivariate - real-valued distributions can be represented via the - MultivariateRealDistribution - interface. + Standard distributions are now available in the + + Commons Statistics component.

- An overview of available continuous distributions:
- Overview of continuous distributions -

- - -

- The distribution framework provides the means to compute probability density - functions (density(·)), probability mass functions - (probability(·)) and distribution functions - (cumulativeProbability(·)) for both - discrete (integer-valued) and continuous probability distributions. - The framework also allows for the computation of inverse cumulative probabilities - and sampling from distributions. -

-

- For an instance f of a distribution F, - and a domain value, x, f.cumulativeProbability(x) - computes P(X <= x) where X is a random variable distributed - as f, i.e., f.cumulativeProbability(·) represents - the distribution function of f. If f is continuous, - (implementing the RealDistribution interface) the probability density - function of f is represented by f.density(·). - For discrete f (implementing IntegerDistribution), the probability - mass function is represented by f.probability(·). Continuous - distributions also implement probability(·) with the same - definition (f.probability(x) represents P(X = x) - where X is distributed as f), though in the continuous - case, this will usually be identically 0. -

-TDistribution t = new TDistribution(29); -double lowerTail = t.cumulativeProbability(-2.656); // P(T(29) <= -2.656) -double upperTail = 1.0 - t.cumulativeProbability(2.75); // P(T(29) >= 2.75) -

- All distributions implement a sample() method to support random sampling from the - distribution. Implementation classes expose constructors allowing the default - RandomGenerator - used by the sampling algorithm to be overridden. If sampling is not going to be used, providing - a null RandomGenerator constructor argument will avoid the overhead of initializing - the default generator. + Commons Math provides +

Inverse distribution functions can be computed using the inverseCumulativeProbability methods. For continuous f and p a probability, f.inverseCumulativeProbability(p) returns

    -
  • inf{x in R | P(X≤x) ≥ p} for 0 < p < 1},
    • -
  • inf{x in R | P(X≤x) > 0} for p = 0}.
    • +
  • inf{x in R | P(X≤x) ≥ p} for 0 < p < 1,
    • +
  • inf{x in R | P(X≤x) > 0} for p = 0.
where X is distributed as f.
For discrete f, the definition is the same, with Z (the integers) in place of R. Note that in the discrete case, the ≥ in the definition can make a difference when p is an attained value of the distribution.

- - -

- User-defined distributions can be implemented using - RealDistribution, - IntegerDistribution and - MultivariateRealDistribution - interfaces serve as base types. These serve as the basis for all the distributions directly supported by - Apache Commons Math. To aid in implementing distributions, - the AbstractRealDistribution, - AbstractIntegerDistribution and - AbstractMultivariateRealDistribution - provide implementation building blocks and offer basic distribution functionality. - By extending these abstract classes directly, much of the repetitive distribution - implementation is already developed and should save time and effort in developing - user-defined distributions. -

-
diff --git a/src/site/xdoc/userguide/index.xml b/src/site/xdoc/userguide/index.xml index 81bdd226f..2608aa814 100644 --- a/src/site/xdoc/userguide/index.xml +++ b/src/site/xdoc/userguide/index.xml @@ -103,8 +103,6 @@
  • 8. Probability Distributions
  • 9. Fractions