## cern.jet.random Class ParetoII

java.lang.Object
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+--cern.colt.PersistentObject
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+--cern.jet.random.AbstractDistribution
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+--cern.jet.random.AbstractContinousDistribution
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+--cern.jet.random.ParetoII
All Implemented Interfaces:
java.lang.Cloneable, cern.colt.function.DoubleFunction, cern.colt.function.IntFunction, java.io.Serializable

public class ParetoII
extends AbstractContinousDistribution

Pareto II Distribution is modified Pareto Distribution by left shift along the x-axis. For Pareto Distribution, see the math definition animated definition.

p(x) = shape*scale^shape*(x+shift)^{-(1+shape)} for x >= scale, shape > 0.

Note that mean is infinite if shape <= 1 and variance is infinite if shape <= 2.

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.

Serialized Form

 Field Summary protected  double pwr protected  double scale protected  double shape protected static ParetoII shared protected  double shift

 Fields inherited from class cern.jet.random.AbstractDistribution randomGenerator

 Constructor Summary ParetoII(double k, double alpha, double mu, RandomElement randomGenerator)           Constructs a ParetoII distribution.

 Method Summary double cdf(double x)           Returns the cumulative distribution function. double nextDouble()           Returns a random number from the distribution. double nextDouble(double k, double alpha, double mu)           Returns a random number from the distribution; bypasses the internal state. double pdf(double x)           Returns the probability distribution function. void setState(double k, double alpha, double mu)           Sets the parameters. static double staticNextDouble(double k, double alpha, double mu)           Returns a random number from the distribution with the given scale = k, and shape = alpha. java.lang.String toString()           Returns a String representation of the receiver.

 Methods inherited from class cern.jet.random.AbstractDistribution apply, apply, clone, getRandomGenerator, makeDefaultGenerator, nextInt, setRandomGenerator

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

 Field Detail

### scale

protected double scale

### shape

protected double shape

### shift

protected double shift

### pwr

protected double pwr

### shared

protected static ParetoII shared
 Constructor Detail

### ParetoII

public ParetoII(double k,
double alpha,
double mu,
RandomElement randomGenerator)
Constructs a ParetoII distribution.

 Method Detail

### cdf

public double cdf(double x)
Returns the cumulative distribution function.

### nextDouble

public double nextDouble()
Returns a random number from the distribution.

Specified by:
nextDouble in class AbstractDistribution

### nextDouble

public double nextDouble(double k,
double alpha,
double mu)
Returns a random number from the distribution; bypasses the internal state.

### pdf

public double pdf(double x)
Returns the probability distribution function.

### setState

public void setState(double k,
double alpha,
double mu)
Sets the parameters.

### staticNextDouble

public static double staticNextDouble(double k,
double alpha,
double mu)
Returns a random number from the distribution with the given scale = k, and shape = alpha.

### toString

public java.lang.String toString()
Returns a String representation of the receiver.

Overrides:
toString in class java.lang.Object