The Pareto distribution Random Number Generator (RNG). More...

#include "random-variable-stream.h"

Inheritance diagram for ns3::ParetoRandomVariable:

Collaboration diagram for ns3::ParetoRandomVariable:

Public Member Functions
	ParetoRandomVariable ()
	Creates a Pareto distribution RNG with the default values for the mean, the shape, and upper bound. More...

double	GetBound () const
	Returns the upper bound on values that can be returned by this RNG stream. More...

virtual uint32_t	GetInteger ()
	Get the next random value drawn from the distribution. More...

uint32_t	GetInteger (uint32_t scale, uint32_t shape, uint32_t bound)
	Get the next random value drawn from the distribution. More...

double	GetScale () const
	Returns the scale parameter for the Pareto distribution returned by this RNG stream. More...

double	GetShape () const
	Returns the shape parameter for the Pareto distribution returned by this RNG stream. More...

double	GetValue () override
	Get the next random value drawn from the distribution. More...

double	GetValue (double scale, double shape, double bound)
	Get the next random value drawn from the distribution. More...

Public Member Functions inherited from ns3::RandomVariableStream
	RandomVariableStream ()
	Default constructor. More...

	RandomVariableStream (const RandomVariableStream &)=delete

	~RandomVariableStream () override
	Destructor. More...

int64_t	GetStream () const
	Returns the stream number for the RngStream. More...

bool	IsAntithetic () const
	Check if antithetic values will be generated. More...

RandomVariableStream &	operator= (const RandomVariableStream &)=delete

void	SetAntithetic (bool isAntithetic)
	Specify whether antithetic values should be generated. More...

void	SetStream (int64_t stream)
	Specifies the stream number for the RngStream. More...

Public Member Functions inherited from ns3::Object
	Object ()
	Constructor. More...

	~Object () override
	Destructor. More...

void	AggregateObject (Ptr< Object > other)
	Aggregate two Objects together. More...

void	Dispose ()
	Dispose of this Object. More...

AggregateIterator	GetAggregateIterator () const
	Get an iterator to the Objects aggregated to this one. More...

TypeId	GetInstanceTypeId () const override
	Get the most derived TypeId for this Object. More...

template<typename T >
Ptr< T >	GetObject () const
	Get a pointer to the requested aggregated Object. More...

template<>
Ptr< Object >	GetObject () const
	Specialization of () for objects of type ns3::Object. More...

template<typename T >
Ptr< T >	GetObject (TypeId tid) const
	Get a pointer to the requested aggregated Object by TypeId. More...

template<>
Ptr< Object >	GetObject (TypeId tid) const
	Specialization of (TypeId tid) for objects of type ns3::Object. More...

void	Initialize ()
	Invoke DoInitialize on all Objects aggregated to this one. More...

bool	IsInitialized () const
	Check if the object has been initialized. More...

Public Member Functions inherited from ns3::SimpleRefCount< Object, ObjectBase, ObjectDeleter >
	SimpleRefCount ()
	Default constructor. More...

	SimpleRefCount (const SimpleRefCount &o[[maybe_unused]])
	Copy constructor. More...

uint32_t	GetReferenceCount () const
	Get the reference count of the object. More...

SimpleRefCount &	operator= (const SimpleRefCount &o[[maybe_unused]])
	Assignment operator. More...

void	Ref () const
	Increment the reference count. More...

void	Unref () const
	Decrement the reference count. More...

Public Member Functions inherited from ns3::ObjectBase
virtual	~ObjectBase ()
	Virtual destructor. More...

void	GetAttribute (std::string name, AttributeValue &value) const
	Get the value of an attribute, raising fatal errors if unsuccessful. More...

bool	GetAttributeFailSafe (std::string name, AttributeValue &value) const
	Get the value of an attribute without raising errors. More...

void	SetAttribute (std::string name, const AttributeValue &value)
	Set a single attribute, raising fatal errors if unsuccessful. More...

bool	SetAttributeFailSafe (std::string name, const AttributeValue &value)
	Set a single attribute without raising errors. More...

bool	TraceConnect (std::string name, std::string context, const CallbackBase &cb)
	Connect a TraceSource to a Callback with a context. More...

bool	TraceConnectWithoutContext (std::string name, const CallbackBase &cb)
	Connect a TraceSource to a Callback without a context. More...

bool	TraceDisconnect (std::string name, std::string context, const CallbackBase &cb)
	Disconnect from a TraceSource a Callback previously connected with a context. More...

bool	TraceDisconnectWithoutContext (std::string name, const CallbackBase &cb)
	Disconnect from a TraceSource a Callback previously connected without a context. More...

Static Public Member Functions
static TypeId	GetTypeId ()
	Register this type. More...

Static Public Member Functions inherited from ns3::RandomVariableStream
static TypeId	GetTypeId ()
	Register this type. More...

Static Public Member Functions inherited from ns3::Object
static TypeId	GetTypeId ()
	Register this type. More...

Static Public Member Functions inherited from ns3::ObjectBase
static TypeId	GetTypeId ()
	Get the type ID. More...

Private Attributes
double	m_bound
	The upper bound on values that can be returned by this RNG stream. More...

double	m_scale
	The scale parameter for the Pareto distribution returned by this RNG stream. More...

double	m_shape
	The shape parameter for the Pareto distribution returned by this RNG stream. More...

Additional Inherited Members
Protected Member Functions inherited from ns3::RandomVariableStream
RngStream *	Peek () const
	Get the pointer to the underlying RngStream. More...

Protected Member Functions inherited from ns3::Object
	Object (const Object &o)
	Copy an Object. More...

virtual void	DoDispose ()
	Destructor implementation. More...

virtual void	DoInitialize ()
	Initialize() implementation. More...

virtual void	NotifyNewAggregate ()
	Notify all Objects aggregated to this one of a new Object being aggregated. More...

Protected Member Functions inherited from ns3::ObjectBase
void	ConstructSelf (const AttributeConstructionList &attributes)
	Complete construction of ObjectBase; invoked by derived classes. More...

virtual void	NotifyConstructionCompleted ()
	Notifier called once the ObjectBase is fully constructed. More...

Related Functions inherited from ns3::ObjectBase
static TypeId	GetObjectIid ()
	Ensure the TypeId for ObjectBase gets fully configured to anchor the inheritance tree properly. More...

Detailed Description

The Pareto distribution Random Number Generator (RNG).

This class supports the creation of objects that return random numbers from a fixed Pareto distribution. It also supports the generation of single random numbers from various Pareto distributions.

The probability density function of a Pareto variable is:

$P(x; x_m, \alpha) dx = \alpha \frac{x_m^\alpha}{x^{\alpha + 1}} dx, \\ \quad x \in [x_m, +\infty)$

where the minimum value is called the Scale parameter and $\alpha > 0$ is called the Pareto index or Shape parameter.

The resulting distribution will have mean

$\mu = x_m \frac{\alpha}{\alpha - 1} \mbox{ for $\alpha > 1$}$

and variance

$\sigma^2 = x_m \frac{1}{(\alpha - 1)(\alpha - 2)} \mbox { for $\alpha > 2$}$

The minimum value can be inferred from the desired mean $\mu$ and the parameter $\alpha$ with the equation

$x_m = \mu \frac{\alpha - 1}{\alpha} \mbox{ for $\alpha > 1$}$

The Pareto RNG value is generated by

$x = \frac{x_m}{u^{\frac{1}{\alpha}}}$

where is a uniform random variable on [0,1).

Bounded Distribution

Since Pareto distributions can theoretically return unbounded values, it is sometimes useful to specify a fixed upper Bound. The bounded version is defined over the interval $x \in [x_m, b]$ . Note however when the upper limit is specified, the mean of the resulting distribution is slightly smaller than the mean value in the unbounded case.

Example

Here is an example of how to use this class:

double scale = 5.0;
double shape = 2.0;
 
Ptr<ParetoRandomVariable> x = CreateObject<ParetoRandomVariable> ();
x->SetAttribute ("Scale", DoubleValue (scale));
x->SetAttribute ("Shape", DoubleValue (shape));
 
double value = x->GetValue ();