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 NakagamiDist:

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Collaboration diagram for NakagamiDist:

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Public Member Functions
	NakagamiDist (double a, double lambda, double c)
	Constructs a `NakagamiDist` object with parameters \(a =\) `a`, \(\lambda=\) `lambda` and \(c =\) `c`.

double	density (double x)

double	cdf (double x)
	Returns the distribution function \(F(x)\). More...

double	barF (double x)
	Returns \(\bar{F}(x) = 1 - F(x)\). More...

double	inverseF (double u)
	Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ). More...

double	getMean ()
	Returns the mean of the distribution function.

double	getVariance ()
	Returns the variance of the distribution function.

double	getStandardDeviation ()
	Returns the standard deviation of the distribution function.

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

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

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

void	setParams (double a, double lambda, double c)
	Sets the parameters \(a\), \(\lambda\) and \(c\) of this object. More...

double []	getParams ()
	Return a table containing the parameters of the current distribution. More...

String	toString ()
	Returns a `String` containing information about the current distribution. More...

Public Member Functions inherited from ContinuousDistribution
abstract double	density (double x)
	Returns \(f(x)\), the density evaluated at \(x\). More...

double	barF (double x)
	Returns the complementary distribution function. More...

double	inverseBrent (double a, double b, double u, double tol)
	Computes the inverse distribution function \(x = F^{-1}(u)\), using the Brent-Dekker method. More...

double	inverseBisection (double u)
	Computes and returns the inverse distribution function \(x = F^{-1}(u)\), using bisection. More...

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

double	getMean ()
	Returns the mean. More...

double	getVariance ()
	Returns the variance. More...

double	getStandardDeviation ()
	Returns the standard deviation. More...

double	getXinf ()
	Returns \(x_a\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...

double	getXsup ()
	Returns \(x_b\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...

void	setXinf (double xa)
	Sets the value \(x_a=\) `xa`, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...

void	setXsup (double xb)
	Sets the value \(x_b=\) `xb`, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...

Static Public Member Functions
static double	density (double a, double lambda, double c, double x)
	Computes the density function of the Nakagami distribution. More...

static double	cdf (double a, double lambda, double c, double x)
	Computes the distribution function. More...

static double	barF (double a, double lambda, double c, double x)
	Computes the complementary distribution function. More...

static double	inverseF (double a, double lambda, double c, double u)
	Computes the inverse of the distribution function. More...

static double	getMean (double a, double lambda, double c)
	Computes and returns the mean \[ E[X] = a + \frac{1}{\sqrt{\lambda}}\; \frac{\Gamma(c+1/2)}{\Gamma(c)}. \] . More...

static double	getVariance (double a, double lambda, double c)
	Computes and returns the variance \[ \mbox{Var}[X] = \frac{1}{\lambda} \left[c - \left(\frac{\Gamma(c+1/2)}{\Gamma(c)}\right)^2\right]. \] . More...

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

Protected Attributes
double	a

double	lambda

double	c

Protected Attributes inherited from ContinuousDistribution
double	supportA = Double.NEGATIVE_INFINITY

double	supportB = Double.POSITIVE_INFINITY

Additional Inherited Members
Public Attributes inherited from ContinuousDistribution
int	decPrec = 15

Static Protected Attributes inherited from ContinuousDistribution
static final double	XBIG = 100.0

static final double	XBIGM = 1000.0

static final double []	EPSARRAY

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.

Member Function Documentation

◆ barF() [1/2]

double barF ( double x )

Returns \(\bar{F}(x) = 1 - F(x)\).

Parameters

x	value at which the complementary distribution function is evaluated

Returns: complementary distribution function evaluated at x

Implements Distribution.

◆ barF() [2/2]

static double 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

◆ cdf() [1/2]

double 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 Distribution.

◆ cdf() [2/2]

static double 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

◆ density()

static double 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

◆ getA()

double getA ( )

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

Returns: returns the location parameter

◆ getC()

double getC ( )

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

Returns: returns the shape parameter

◆ getLambda()

double getLambda ( )

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

Returns: returns the scale parameter

◆ getMean()

static double 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

◆ getParams()

double [] 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 Distribution.

◆ getStandardDeviation()

static double 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

◆ getVariance()

static double 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

◆ inverseF() [1/2]

double inverseF ( double u )

Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ).

Parameters

u	value in the interval \((0,1)\) for which the inverse distribution function is evaluated

Returns: the inverse distribution function evaluated at u

Implements Distribution.

◆ inverseF() [2/2]

static double 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

◆ setParams()

void 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

◆ toString()

String toString ( )

Returns a String containing information about the current distribution.

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

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

NakagamiDist.java

Public Member Functions

Static Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ barF() [1/2]

◆ barF() [2/2]

◆ cdf() [1/2]

◆ cdf() [2/2]

◆ density()

◆ getA()

◆ getC()

◆ getLambda()

◆ getMean()

◆ getParams()

◆ getStandardDeviation()

◆ getVariance()

◆ inverseF() [1/2]

◆ inverseF() [2/2]

◆ setParams()

◆ toString()