NakagamiDist (Java Libraries for Stochastic Simulation)

java.lang.Object
- umontreal.iro.lecuyer.probdist.ContinuousDistribution
- - umontreal.iro.lecuyer.probdist.NakagamiDist

All Implemented Interfaces:

Distribution
```
public class NakagamiDist
extends ContinuousDistribution
```
Extends the class ContinuousDistribution for the Nakagami distribution with location parameter a, scale parameter λ > 0 and shape parameter c > 0. The density is

f (x) = 2λ^c/Γ(c) (x - a)^2c-1 e^-λ(x-a)² for x > a,

f (x) = 0 for x <= a,
where Γ is the gamma function.

Field Summary
- Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
  decPrec

Constructor Summary

Constructors
Constructor and Description
`NakagamiDist(double a, double lambda, double c)` Constructs a `NakagamiDist` object with parameters a = `a`, λ = `lambda` and c = `c`.

Method Summary

Methods
Modifier and Type	Method and Description
`double`	`barF(double x)` Returns the complementary distribution function.
`static double`	`barF(double a, double lambda, double c, double x)` Computes the complementary distribution function.
`double`	`cdf(double x)` Returns the distribution function F(x).
`static double`	`cdf(double a, double lambda, double c, double x)` Computes the distribution function.
`double`	`density(double x)` Returns f (x), the density evaluated at x.
`static double`	`density(double a, double lambda, double c, double x)` Computes the density function of the Nakagami distribution.
`double`	`getA()` Returns the location parameter a of this object.
`double`	`getC()` Returns the shape parameter c of this object.
`double`	`getLambda()` Returns the scale parameter λ of this object.
`double`	`getMean()` Returns the mean.
`static double`	`getMean(double a, double lambda, double c)` .
`double[]`	`getParams()` Return a table containing the parameters of the current distribution.
`double`	`getStandardDeviation()` Returns the standard deviation.
`static double`	`getStandardDeviation(double a, double lambda, double c)` Computes the standard deviation of the Nakagami distribution with parameters a, λ and c.
`double`	`getVariance()` Returns the variance.
`static double`	`getVariance(double a, double lambda, double c)` .
`double`	`inverseF(double u)` Returns the inverse distribution function x = F^-1(u).
`static double`	`inverseF(double a, double lambda, double c, double u)` Computes the inverse of the distribution function.
`void`	`setParams(double a, double lambda, double c)` Sets the parameters a, λ and c of this object.
`java.lang.String`	`toString()` Returns a `String` containing information about the current distribution.

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup

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

- Constructor Detail
  - NakagamiDist
```
public NakagamiDist(double a,
            double lambda,
            double c)
```
    Constructs a NakagamiDist object with parameters a = a, λ = lambda and c = c.
- Method Detail
  - density
```
public double density(double x)
```
    Description copied from class: ContinuousDistribution
    
    Returns f (x), the density evaluated at x.
    
    Specified by:
    
    density in class ContinuousDistribution
    
    Parameters:
    x - value at which the density is evaluated
    
    Returns:
    density function evaluated at x
  - cdf
```
public double cdf(double x)
```
    Description copied from interface: Distribution
    
    Returns the distribution function F(x).
    
    Parameters:
    x - value at which the distribution function is evaluated
    
    Returns:
    distribution function evaluated at x
  - barF
```
public double barF(double x)
```
    Description copied from class: ContinuousDistribution
    
    Returns the complementary distribution function. The default implementation computes bar(F)(x) = 1 - F(x).
    
    Specified by:
    
    barF in interface Distribution
    
    Overrides:
    
    barF in class ContinuousDistribution
    
    Parameters:
    x - value at which the complementary distribution function is evaluated
    
    Returns:
    complementary distribution function evaluated at x
  - inverseF
```
public double inverseF(double u)
```
    Description copied from class: ContinuousDistribution
    
    Returns the inverse distribution function x = F^-1(u). Restrictions: u∈[0, 1].
    
    Specified by:
    
    inverseF in interface Distribution
    
    Overrides:
    
    inverseF in class ContinuousDistribution
    
    Parameters:
    u - value at which the inverse distribution function is evaluated
    
    Returns:
    the inverse distribution function evaluated at u
  - getMean
```
public double getMean()
```
    Description copied from class: ContinuousDistribution
    
    Returns the mean.
    
    Specified by:
    
    getMean in interface Distribution
    
    Overrides:
    
    getMean in class ContinuousDistribution
    
    Returns:
    the mean
  - getVariance
```
public double getVariance()
```
    Description copied from class: ContinuousDistribution
    
    Returns the variance.
    
    Specified by:
    
    getVariance in interface Distribution
    
    Overrides:
    
    getVariance in class ContinuousDistribution
    
    Returns:
    the variance
  - getStandardDeviation
```
public double getStandardDeviation()
```
    Description copied from class: ContinuousDistribution
    
    Returns the standard deviation.
    
    Specified by:
    
    getStandardDeviation in interface Distribution
    
    Overrides:
    
    getStandardDeviation in class ContinuousDistribution
    
    Returns:
    the standard deviation
  - density
```
public static double density(double a,
             double lambda,
             double c,
             double x)
```
    Computes the density function of the Nakagami distribution.
    
    Parameters:
    a - the location parameter
    lambda - the scale parameter
    c - the shape parameter
    x - the value at which the density is evaluated
    
    Returns:
    returns the density function
  - cdf
```
public static double cdf(double a,
         double lambda,
         double c,
         double x)
```
    Computes the distribution function.
    
    Parameters:
    a - the location parameter
    lambda - the scale parameter
    c - the shape parameter
    x - the value at which the distribution is evaluated
    
    Returns:
    returns the cdf function
  - barF
```
public static double barF(double a,
          double lambda,
          double c,
          double x)
```
    Computes the complementary distribution function.
    
    Parameters:
    a - the location parameter
    lambda - the scale parameter
    c - the shape parameter
    x - the value at which the complementary distribution is evaluated
    
    Returns:
    returns the complementary distribution function
  - inverseF
```
public static double inverseF(double a,
              double lambda,
              double c,
              double u)
```
    Computes the inverse of the distribution function.
    
    Parameters:
    a - the location parameter
    lambda - the scale parameter
    c - the shape parameter
    u - the value at which the inverse distribution is evaluated
    
    Returns:
    returns the inverse distribution function
  - getMean
```
public static double getMean(double a,
             double lambda,
             double c)
```
    . Computes and returns the mean
    
    E[X] = a + $\displaystyle {\frac{{1}}{{\sqrt{\lambda}}}}$ $\displaystyle {\frac{{\Gamma(c+1/2)}}{{\Gamma(c)}}}$ .
    
    Parameters:
    a - the location parameter
    lambda - the scale parameter
    c - the shape parameter
    
    Returns:
    returns the mean
  - getVariance
```
public static double getVariance(double a,
                 double lambda,
                 double c)
```
    . Computes and returns the variance
    
    Var[X] = $\displaystyle {\frac{{1}}{{\lambda}}}$ [c - ([tex2html_wrap_indisplay261])²].
    
    Parameters:
    a - the location parameter
    lambda - the scale parameter
    c - the shape parameter
    
    Returns:
    returns the variance
  - getStandardDeviation
```
public static double getStandardDeviation(double a,
                          double lambda,
                          double c)
```
    Computes the standard deviation of the Nakagami distribution with parameters a, λ and c.
    
    Parameters:
    a - the location parameter
    lambda - the scale parameter
    c - the shape parameter
    
    Returns:
    returns the standard deviation
  - getA
```
public double getA()
```
    Returns the location parameter a of this object.
    
    Returns:
    returns the location parameter
  - getLambda
```
public double getLambda()
```
    Returns the scale parameter λ of this object.
    
    Returns:
    returns the scale parameter
  - getC
```
public double getC()
```
    Returns the shape parameter c of this object.
    
    Returns:
    returns the shape parameter
  - setParams
```
public void setParams(double a,
             double lambda,
             double c)
```
    Sets the parameters a, λ and c of this object.
    
    Parameters:
    a - the location parameter
    lambda - the scale parameter
    c - the shape parameter
  - getParams
```
public double[] getParams()
```
    Return a table containing the parameters of the current distribution. This table is put in regular order: [a, λ, c].
    
    Returns:
    returns the parameters [a, λ, c]
  - toString
```
public java.lang.String toString()
```
    Returns a String containing information about the current distribution.
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    returns a String containing information about the current distribution.

Class NakagamiDist

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

Constructor Summary

Method Summary

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

Methods inherited from class java.lang.Object

Constructor Detail

NakagamiDist

Method Detail

density

cdf

barF

inverseF

getMean

getVariance

getStandardDeviation

density

cdf

barF

inverseF

getMean

getVariance

getStandardDeviation

getA

getLambda

getC

setParams

getParams

toString