EmpiricalWalker
cern.jet.random

## Class EmpiricalWalker

• All Implemented Interfaces:
DoubleFunction, IntFunction, Serializable, Cloneable

```public class EmpiricalWalker
extends AbstractDiscreteDistribution```
Discrete Empirical distribution (pdf's can be specified).

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.

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: Walker's algorithm. Generating a random number takes O(1), i.e. constant time, as opposed to commonly used algorithms with logarithmic time complexity. Preprocessing time (on object construction) is O(k) where k is the number of elements of the provided empirical pdf. Space complexity is O(k).

This is a port of discrete.c which was written by James Theiler and is distributed with GSL 0.4.1. Theiler's implementation in turn is based upon

Alastair J. Walker, An efficient method for generating discrete random variables with general distributions, ACM Trans Math Soft 3, 253-256 (1977).

See also: D. E. Knuth, The Art of Computer Programming, Volume 2 (Seminumerical algorithms), 3rd edition, Addison-Wesley (1997), p120.

Serialized Form

• ### Fields inherited from class cern.colt.PersistentObject

`serialVersionUID`
• ### Constructor Summary

Constructors
Constructor and Description
```EmpiricalWalker(double[] pdf, int interpolationType, RandomEngine randomGenerator)```
Constructs an Empirical distribution.
• ### Method Summary

Methods
Modifier and Type Method and Description
`double` `cdf(int k)`
Returns the cumulative distribution function.
`Object` `clone()`
Returns a deep copy of the receiver; the copy will produce identical sequences.
`int` `nextInt()`
Returns a random integer k with probability pdf(k).
`double` `pdf(int k)`
Returns the probability distribution function.
`void` ```setState(double[] pdf, int interpolationType)```
Sets the distribution parameters.
`void` `setState2(double[] pdf)`
Sets the distribution parameters.
`String` `toString()`
Returns a String representation of the receiver.
• ### Methods inherited from class cern.jet.random.AbstractDiscreteDistribution

`nextDouble`
• ### Methods inherited from class cern.jet.random.AbstractDistribution

`apply, apply, makeDefaultGenerator`
• ### Methods inherited from class java.lang.Object

`equals, getClass, hashCode, notify, notifyAll, wait, wait, wait`
• ### Constructor Detail

• #### EmpiricalWalker

```public EmpiricalWalker(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:
• #### nextInt

`public int nextInt()`
Returns a random integer k with probability pdf(k).
Specified by:
`nextInt` in class `AbstractDiscreteDistribution`
• #### 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 all of the following conditions
• pdf != null && pdf.length > 0
• 0.0 <= pdf[i] : 0 < =i <= pdf.length-1
• 0.0 < Sum(pdf[i]) : 0 <=i <= pdf.length-1
Parameters:
`pdf` - probability distribution function.
Throws:
`IllegalArgumentException` - if at least one of the three conditions above is violated.
• #### setState2

`public void setState2(double[] pdf)`
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.
Throws:
`IllegalArgumentException` - if at least one of the three conditions above is violated.
• #### toString

`public String toString()`
Returns a String representation of the receiver.
Overrides:
`toString` in class `Object`