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umontreal.iro.lecuyer.probdist
Class NakagamiDist

java.lang.Object
  extended by umontreal.iro.lecuyer.probdist.ContinuousDistribution
      extended by 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) = 2λc/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
NakagamiDist(double a, double lambda, double c)
          Constructs a NakagamiDist object with parameters a = a, λ = lambda and c = c.
 
Method Summary
 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.
 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_indisplay259])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 String toString()
Returns a String containing information about the current distribution.

Overrides:
toString in class Object
Returns:
returns a String containing information about the current distribution.
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