SSJ
V. 2.6.

## umontreal.iro.lecuyer.probdist Class NakagamiDist

```java.lang.Object
umontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.NakagamiDist
```
All Implemented Interfaces:
Distribution

`public class NakagamiDistextends 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 + 1#1  2#2.

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] = 3#3[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.

SSJ
V. 2.6.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.