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## cern.jet.random
Class Empirical

    java.lang.Object
      cern.colt.PersistentObject
          cern.jet.random.AbstractDistribution
              cern.jet.random.AbstractContinousDistribution
                  cern.jet.random.Empirical

All Implemented Interfaces:
  Cloneable, DoubleFunction, IntFunction, Serializable

public class Empirical
extends AbstractContinousDistribution

Empirical distribution.

The probability distribution function (pdf) must be provided by the user as an array of positive real numbers. The pdf does not need to be provided in the form of relative probabilities, absolute probabilities are also accepted.

If `interpolationType == LINEAR_INTERPOLATION` a linear interpolation within the bin is computed, resulting in a constant density within each bin.

If `interpolationType == NO_INTERPOLATION` no interpolation is performed and the result is a discrete distribution.

Instance methods operate on a user supplied uniform random number generator; they are unsynchronized.

Static methods operate on a default uniform random number generator; they are synchronized.

Implementation: A uniform random number is generated using a user supplied generator. The uniform number is then transformed to the user's distribution using the cumulative probability distribution constructed from the pdf. The cumulative distribution is inverted using a binary search for the nearest bin boundary.

This is a port of RandGeneral used in CLHEP 1.4.0 (C++).

Version:
  1.0, 09/24/99
See Also:
  Serialized Form

Field Summary
`static int` | `LINEAR_INTERPOLATION`
`static int` | `NO_INTERPOLATION`

Fields inherited from class cern.colt.PersistentObject
`serialVersionUID`

Constructor Summary
`Empirical(double[] pdf, int interpolationType, RandomEngine randomGenerator)` Constructs an Empirical distribution.

Method Summary
`double` | `cdf(int k)` Returns the cumulative distribution function.
`Object` | `clone()` Returns a deep copy of the receiver; the copy will produce identical sequences.
`double` | `nextDouble()` Returns a random number from the distribution.
`double` | `pdf(double x)` Returns the probability distribution function.
`double` | `pdf(int k)` Returns the probability distribution function.
`void` | `setState(double[] pdf, int interpolationType)` Sets the distribution parameters.
`String` | `toString()` Returns a String representation of the receiver.

Methods inherited from class cern.jet.random.AbstractDistribution
`apply, apply, makeDefaultGenerator, nextInt`

Methods inherited from class java.lang.Object
`equals, getClass, hashCode, notify, notifyAll, wait, wait, wait`

Field Detail

### LINEAR_INTERPOLATION

    public static final int LINEAR_INTERPOLATION

See Also:
  Constant Field Values

### NO_INTERPOLATION

    public static final int NO_INTERPOLATION

See Also:
  Constant Field Values

Constructor Detail

### Empirical

    public Empirical(double[] pdf,
                     int interpolationType,
                     RandomEngine randomGenerator)

  Constructs an Empirical distribution. The probability distribution function (pdf) is an array of positive real numbers. It need not be provided in the form of relative probabilities, absolute probabilities are also accepted. The `pdf` must satisfy both of the following conditions
  - `0.0 <= pdf[i] : 0<=i<=pdf.length-1`
  - `0.0 < Sum(pdf[i]) : 0<=i<=pdf.length-1`

Parameters:
  `pdf` - the probability distribution function.
  `interpolationType` - can be either `Empirical.NO_INTERPOLATION` or `Empirical.LINEAR_INTERPOLATION`.
  `randomGenerator` - a uniform random number generator.
Throws:
  `IllegalArgumentException` - if at least one of the three conditions above is violated.

Method Detail

### cdf

    public double cdf(int k)

  Returns the cumulative distribution function.

### clone

    public Object clone()

  Returns a deep copy of the receiver; the copy will produce identical sequences. After this call has returned, the copy and the receiver have equal but separate state.

  Overrides:
    `clone` in class `AbstractDistribution`
  Returns:
    a copy of the receiver.

### nextDouble

    public double nextDouble()

  Returns a random number from the distribution.

  Specified by:
    `nextDouble` in class `AbstractDistribution`

### pdf

    public double pdf(double x)

  Returns the probability distribution function.

### pdf

    public double pdf(int k)

  Returns the probability distribution function.

### setState

    public void setState(double[] pdf,
                         int interpolationType)

  Sets the distribution parameters. The `pdf` must satisfy both of the following conditions
  - `0.0 <= pdf[i] : 0 < =i <= pdf.length-1`
  - `0.0 < Sum(pdf[i]) : 0 <=i <= pdf.length-1`

  Parameters:
    `pdf` - probability distribution function.
    `interpolationType` - can be either `Empirical.NO_INTERPOLATION` or `Empirical.LINEAR_INTERPOLATION`.
  Throws:
    `IllegalArgumentException` - if at least one of the three conditions above is violated.

### toString

    public String toString()

  Returns a String representation of the receiver.

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