Extends the class ContinuousDistribution for the Nakagami distribution with location parameter \(a\), scale parameter \(\lambda> 0\) and shape parameter \(c > 0\). More...

Inheritance diagram for umontreal.ssj.probdist.NakagamiDist:

Public Member Functions
	NakagamiDist (double a, double lambda, double c)
	Constructs a NakagamiDist object with parameters \(a =\) a,.
double	density (double x)
	Returns \(f(x)\), the density evaluated at \(x\).
double	cdf (double x)
	Returns the distribution function \(F(x)\).
double	barF (double x)
	Returns the complementary distribution function.
double	inverseF (double u)
	Returns the inverse distribution function \(x = F^{-1}(u)\).
double	getMean ()
	Returns the mean.
double	getVariance ()
	Returns the variance.
double	getStandardDeviation ()
	Returns the standard deviation.
double	getA ()
	Returns the location parameter \(a\) of this object.
double	getLambda ()
	Returns the scale parameter \(\lambda\) of this object.
double	getC ()
	Returns the shape parameter \(c\) of this object.
void	setParams (double a, double lambda, double c)
	Sets the parameters \(a\), \(\lambda\) and \(c\) of this object.
double[]	getParams ()
	Return a table containing the parameters of the current distribution.
String	toString ()
	Returns a String containing information about the current distribution.
Public Member Functions inherited from umontreal.ssj.probdist.ContinuousDistribution
double	inverseBrent (double a, double b, double u, double tol)
	Computes the inverse distribution function \(x = F^{-1}(u)\), using the Brent-Dekker method.
double	inverseBisection (double u)
	Computes and returns the inverse distribution function \(x = F^{-1}(u)\), using bisection.
double	getXinf ()
	Returns \(x_a\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
double	getXsup ()
	Returns \(x_b\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
void	setXinf (double xa)
	Sets the value \(x_a=\) xa, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
void	setXsup (double xb)
	Sets the value \(x_b=\) xb, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).

Static Public Member Functions
static double	density (double a, double lambda, double c, double x)
	Computes the density function of the Nakagami distribution.
static double	cdf (double a, double lambda, double c, double x)
	Computes the distribution function.
static double	barF (double a, double lambda, double c, double x)
	Computes the complementary distribution function.
static double	inverseF (double a, double lambda, double c, double u)
	Computes the inverse of the distribution function.
static double	getMean (double a, double lambda, double c)
	Computes and returns the mean.
static double	getVariance (double a, double lambda, double c)
	Computes and returns the variance.
static double	getStandardDeviation (double a, double lambda, double c)
	Computes the standard deviation of the Nakagami distribution with parameters \(a\), \(\lambda\) and \(c\).

Detailed Description

Extends the class ContinuousDistribution for the Nakagami distribution with location parameter \(a\), scale parameter \(\lambda> 0\) and shape parameter \(c > 0\).

The density is

\[ f(x) = \frac{2\lambda^c}{\Gamma(c)} (x-a)^{2c-1} e^{-{\lambda}(x-a)^2} \qquad\mbox{for } x > a,\tag{fnakagami} \]

\[ f(x) = 0 \qquad\mbox{ for } x \le a, \]

where \(\Gamma\) is the gamma function.

Definition at line 44 of file NakagamiDist.java.

Constructor & Destructor Documentation

◆ NakagamiDist()

umontreal.ssj.probdist.NakagamiDist.NakagamiDist	(	double	a,
		double	lambda,
		double	c )

Constructs a NakagamiDist object with parameters \(a =\) a,.

\(\lambda=\) lambda and \(c =\) c.

Definition at line 56 of file NakagamiDist.java.

Member Function Documentation

◆ barF() [1/2]

double umontreal.ssj.probdist.NakagamiDist.barF	(	double	a,
		double	lambda,
		double	c,
		double	x )

static

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

Definition at line 140 of file NakagamiDist.java.

◆ barF() [2/2]

double umontreal.ssj.probdist.NakagamiDist.barF ( double x )

Returns the complementary distribution function.

The default implementation computes \(\bar{F}(x) = 1 - F(x)\).

Parameters

x	value at which the complementary distribution function is evaluated

Returns: complementary distribution function evaluated at x

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 70 of file NakagamiDist.java.

◆ cdf() [1/2]

double umontreal.ssj.probdist.NakagamiDist.cdf	(	double	a,
		double	lambda,
		double	c,
		double	x )

static

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

Definition at line 120 of file NakagamiDist.java.

◆ cdf() [2/2]

double umontreal.ssj.probdist.NakagamiDist.cdf ( double x )

Returns the distribution function \(F(x)\).

Parameters

x	value at which the distribution function is evaluated

Returns: distribution function evaluated at x

Implements umontreal.ssj.probdist.Distribution.

Definition at line 66 of file NakagamiDist.java.

◆ density() [1/2]

double umontreal.ssj.probdist.NakagamiDist.density	(	double	a,
		double	lambda,
		double	c,
		double	x )

static

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

Definition at line 99 of file NakagamiDist.java.

◆ density() [2/2]

double umontreal.ssj.probdist.NakagamiDist.density ( double x )

Returns \(f(x)\), the density evaluated at \(x\).

Parameters

x	value at which the density is evaluated

Returns: density function evaluated at x

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 60 of file NakagamiDist.java.

◆ getA()

double umontreal.ssj.probdist.NakagamiDist.getA ( )

Returns the location parameter \(a\) of this object.

Returns: returns the location parameter

Definition at line 227 of file NakagamiDist.java.

◆ getC()

double umontreal.ssj.probdist.NakagamiDist.getC ( )

Returns the shape parameter \(c\) of this object.

Returns: returns the shape parameter

Definition at line 245 of file NakagamiDist.java.

◆ getLambda()

double umontreal.ssj.probdist.NakagamiDist.getLambda ( )

Returns the scale parameter \(\lambda\) of this object.

Returns: returns the scale parameter

Definition at line 236 of file NakagamiDist.java.

◆ getMean() [1/2]

double umontreal.ssj.probdist.NakagamiDist.getMean ( )

Returns the mean.

Returns: the mean

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 78 of file NakagamiDist.java.

◆ getMean() [2/2]

double umontreal.ssj.probdist.NakagamiDist.getMean	(	double	a,
		double	lambda,
		double	c )

static

Computes and returns the mean.

\[ E[X] = a + \frac{1}{\sqrt{\lambda}}\; \frac{\Gamma(c+1/2)}{\Gamma(c)}. \]

Parameters

a	the location parameter
lambda	the scale parameter
c	the shape parameter

Returns: returns the mean

Definition at line 183 of file NakagamiDist.java.

◆ getParams()

double[] umontreal.ssj.probdist.NakagamiDist.getParams ( )

Return a table containing the parameters of the current distribution.

This table is put in regular order: [ \(a\), \(\lambda\), \(c\)].

Returns: returns the parameters [ \(a\), \(\lambda\), \(c\)]

Implements umontreal.ssj.probdist.Distribution.

Definition at line 274 of file NakagamiDist.java.

◆ getStandardDeviation() [1/2]

double umontreal.ssj.probdist.NakagamiDist.getStandardDeviation ( )

Returns the standard deviation.

Returns: the standard deviation

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 86 of file NakagamiDist.java.

◆ getStandardDeviation() [2/2]

double umontreal.ssj.probdist.NakagamiDist.getStandardDeviation	(	double	a,
		double	lambda,
		double	c )

static

Computes the standard deviation of the Nakagami distribution with parameters \(a\), \(\lambda\) and \(c\).

Parameters

a	the location parameter
lambda	the scale parameter
c	the shape parameter

Returns: returns the standard deviation

Definition at line 218 of file NakagamiDist.java.

◆ getVariance() [1/2]

double umontreal.ssj.probdist.NakagamiDist.getVariance ( )

Returns the variance.

Returns: the variance

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 82 of file NakagamiDist.java.

◆ getVariance() [2/2]

double umontreal.ssj.probdist.NakagamiDist.getVariance	(	double	a,
		double	lambda,
		double	c )

static

Computes and returns the variance.

\[ \mbox{Var}[X] = \frac{1}{\lambda} \left[c - \left(\frac{\Gamma(c+1/2)}{\Gamma(c)}\right)^2\right]. \]

Parameters

a	the location parameter
lambda	the scale parameter
c	the shape parameter

Returns: returns the variance

Definition at line 200 of file NakagamiDist.java.

◆ inverseF() [1/2]

double umontreal.ssj.probdist.NakagamiDist.inverseF	(	double	a,
		double	lambda,
		double	c,
		double	u )

static

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

Definition at line 159 of file NakagamiDist.java.

◆ inverseF() [2/2]

double umontreal.ssj.probdist.NakagamiDist.inverseF ( double u )

Returns the inverse distribution function \(x = F^{-1}(u)\).

Restrictions: \(u \in[0,1]\).

Parameters

u	value at which the inverse distribution function is evaluated

Returns: the inverse distribution function evaluated at u

Exceptions

IllegalArgumentException if \(u\) is not in the interval \([0,1]\)

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 74 of file NakagamiDist.java.

◆ setParams()

void umontreal.ssj.probdist.NakagamiDist.setParams	(	double	a,
		double	lambda,
		double	c )

Sets the parameters \(a\), \(\lambda\) and \(c\) of this object.

Parameters

a	the location parameter
lambda	the scale parameter
c	the shape parameter

Definition at line 256 of file NakagamiDist.java.

◆ toString()

String umontreal.ssj.probdist.NakagamiDist.toString ( )

Returns a String containing information about the current distribution.

Returns: returns a String containing information about the current distribution.

Definition at line 285 of file NakagamiDist.java.

The documentation for this class was generated from the following file:

src/main/java/umontreal/ssj/probdist/NakagamiDist.java

SSJ API Documentation Stochastic Simulation in Java

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ NakagamiDist()

Member Function Documentation

◆ barF() [1/2]

◆ barF() [2/2]

◆ cdf() [1/2]

◆ cdf() [2/2]

◆ density() [1/2]

◆ density() [2/2]

◆ getA()

◆ getC()

◆ getLambda()

◆ getMean() [1/2]

◆ getMean() [2/2]

◆ getParams()

◆ getStandardDeviation() [1/2]

◆ getStandardDeviation() [2/2]

◆ getVariance() [1/2]

◆ getVariance() [2/2]

◆ inverseF() [1/2]

◆ inverseF() [2/2]

◆ setParams()

◆ toString()