#include <STK_Law_Weibull.h>

Inheritance diagram for STK::Law::Weibull:

Public Types
typedef IUnivLaw< Real >	Base

Public Member Functions
	Weibull (Real const &k=1., Real const &lambda=1.)
	Default constructor.

virtual	~Weibull ()
	destructor

Real const &	k () const

Real const &	lambda () const

void	setK (Real const &k)

void	setLambda (Real const &lambda)

virtual Real	rand () const

virtual Real	pdf (Real const &x) const

virtual Real	lpdf (Real const &x) const

virtual Real	cdf (Real const &t) const
	The cumulative distribution function for the Weibull distribution is $F(x;k,\lambda) = 1- e^{-(x/\lambda)^k}.$ .

virtual Real	icdf (Real const &p) const
	The quantile (inverse cumulative distribution) function for the Weibull distribution is $Q(p;k,\lambda) = \lambda {(-\ln(1-p))}^{1/k}$ .

Public Member Functions inherited from STK::Law::IUnivLaw< Real >
virtual	~IUnivLaw ()
	Virtual destructor.

virtual Real	lcdf (Real const &t) const
	compute the lower tail log-cumulative distribution function Give the log-probability that a random variate is less or equal to t.

virtual Real	cdfc (Real const &t) const
	calculate the complement of cumulative distribution function, called in statistics the survival function.

virtual Real	lcdfc (Real const &t) const
	calculate the log-complement of cumulative distribution function Give the log-probability that a random variate is greater than t.

Public Member Functions inherited from STK::Law::ILawBase
String const &	name () const

Static Public Member Functions
static Real	rand (Real const &k, Real const &lambda)

static Real	pdf (Real const &x, Real const &k, Real const &lambda)

static Real	lpdf (Real const &x, Real const &k, Real const &lambda)

static Real	cdf (Real const &t, Real const &k, Real const &lambda)

static Real	icdf (Real const &p, Real const &k, Real const &lambda)
	Compute the inverse cumulative distribution function at p of the standard log-normal distribution.

Protected Attributes
Real	k_
	The shape parameter.

Real	lambda_
	The scale parameter.

Protected Attributes inherited from STK::Law::ILawBase
String	name_
	Name of the Law.

Additional Inherited Members
Protected Member Functions inherited from STK::Law::IUnivLaw< Real >
	IUnivLaw (String const &name)
	Constructor.

	IUnivLaw (IUnivLaw const &law)
	copy Constructor.

Protected Member Functions inherited from STK::Law::ILawBase
	ILawBase (String const &name)
	Constructor.

	~ILawBase ()
	destructor.

Detailed Description

Weibull distribution law.

In probability theory and statistics, the Weibull distribution is a continuous probability distribution. It is named after Waloddi Weibull, who described it in detail in 1951.

The probability density function of a Weibull random variable is

$f(x;\lambda,k) = \frac{k}{\lambda}\left(\frac{x}{\lambda}\right)^{k-1}e^{-(x/\lambda)^{k}} \quad x\geq0 ,$

where k > 0 is the shape parameter and $ λ > 0$ is the scale parameter of the distribution.

Definition at line 60 of file STK_Law_Weibull.h.

Member Typedef Documentation

◆ Base

typedef IUnivLaw<Real> STK::Law::Weibull::Base

Definition at line 63 of file STK_Law_Weibull.h.

Constructor & Destructor Documentation

◆ Weibull()

STK::Law::Weibull::Weibull	(	Real const &	k = `1.`,
		Real const &	lambda = `1.`
	)

inline

Default constructor.

Parameters

k,lambda shape and scale (dispersion) parameters

Definition at line 67 of file STK_Law_Weibull.h.

68 : Base(_T("Weibull")), k_(k), lambda_(lambda)

69 {}

_T

#define _T(x)

Let x unmodified.

Definition STK_Typedefs.h:71

STK::Law::Weibull::Base

IUnivLaw< Real > Base

Definition STK_Law_Weibull.h:63

STK::Law::Weibull::k

Real const & k() const

Definition STK_Law_Weibull.h:73

STK::Law::Weibull::lambda_

Real lambda_

The scale parameter.

Definition STK_Law_Weibull.h:151

STK::Law::Weibull::lambda

Real const & lambda() const

Definition STK_Law_Weibull.h:75

STK::Law::Weibull::k_

Real k_

The shape parameter.

Definition STK_Law_Weibull.h:149

◆ ~Weibull()

virtual STK::Law::Weibull::~Weibull ( )

inlinevirtual

destructor

Definition at line 71 of file STK_Law_Weibull.h.

71{}

Member Function Documentation

◆ cdf() [1/2]

Real STK::Law::Weibull::cdf ( Real const & t ) const

virtual

The cumulative distribution function for the Weibull distribution is $F(x;k,\lambda) = 1- e^{-(x/\lambda)^k}.$ .

Returns: the cumulative distribution function

Parameters

t	a positive real value

Implements STK::Law::IUnivLaw< Real >.

Definition at line 71 of file STK_Law_Weibull.cpp.

{
  return 0;
}

◆ cdf() [2/2]

Real STK::Law::Weibull::cdf	(	Real const &	t,
		Real const &	k,
		Real const &	lambda
	)

static

Returns: the cumulative distribution function

Parameters

t	a positive real value
k,lambda	shape and scale (dispersion) parameters

Definition at line 112 of file STK_Law_Weibull.cpp.

{
  return 0;
}

◆ icdf() [1/2]

Real STK::Law::Weibull::icdf ( Real const & p ) const

virtual

The quantile (inverse cumulative distribution) function for the Weibull distribution is $Q(p;k,\lambda) = \lambda {(-\ln(1-p))}^{1/k}$ .

Returns: the inverse cumulative distribution function

Parameters

p	a probability number

Implements STK::Law::IUnivLaw< Real >.

Definition at line 80 of file STK_Law_Weibull.cpp.

{
  return 0;
}

◆ icdf() [2/2]

Real STK::Law::Weibull::icdf	(	Real const &	p,
		Real const &	k,
		Real const &	lambda
	)

static

Compute the inverse cumulative distribution function at p of the standard log-normal distribution.

Parameters

p	a probability number.
k,lambda	shape and scale (dispersion) parameters

Returns: the inverse cumulative distribution function value at p.

Definition at line 123 of file STK_Law_Weibull.cpp.

{
  return 0;
}

◆ k()

Real const & STK::Law::Weibull::k ( ) const

inline

Returns: shape parameter

Definition at line 73 of file STK_Law_Weibull.h.

73{ return k_;}

References k_.

Referenced by setK().

◆ lambda()

Real const & STK::Law::Weibull::lambda ( ) const

inline

Returns: scale parameter

Definition at line 75 of file STK_Law_Weibull.h.

75{ return lambda_;}

References lambda_.

Referenced by setLambda().

◆ lpdf() [1/2]

Real STK::Law::Weibull::lpdf ( Real const & x ) const

virtual

Returns: the value of the log-pdf

Parameters

x	a positive real value

Reimplemented from STK::Law::IUnivLaw< Real >.

Definition at line 62 of file STK_Law_Weibull.cpp.

{
  return 0;
}

◆ lpdf() [2/2]

Real STK::Law::Weibull::lpdf	(	Real const &	x,
		Real const &	k,
		Real const &	lambda
	)

static

Returns: the value of the log-pdf

Parameters

x	a positive real value
k,lambda	shape and scale (dispersion) parameters

Definition at line 104 of file STK_Law_Weibull.cpp.

{
  return 0;
}

◆ pdf() [1/2]

Real STK::Law::Weibull::pdf ( Real const & x ) const

virtual

Returns: the value of the pdf

Parameters

x	a positive real value

Implements STK::Law::IUnivLaw< Real >.

Definition at line 55 of file STK_Law_Weibull.cpp.

{
  return 0;
}

◆ pdf() [2/2]

Real STK::Law::Weibull::pdf	(	Real const &	x,
		Real const &	k,
		Real const &	lambda
	)

static

Returns: the value of the pdf

Parameters

x	a positive real value
k,lambda	shape and scale (dispersion) parameters

Definition at line 96 of file STK_Law_Weibull.cpp.

{
  return 0;
}

◆ rand() [1/2]

Real STK::Law::Weibull::rand ( ) const

virtual

Returns: a pseudo Weibull random variate.

Implements STK::Law::IUnivLaw< Real >.

Definition at line 48 of file STK_Law_Weibull.cpp.

{
  return 0;
}

◆ rand() [2/2]

Real STK::Law::Weibull::rand	(	Real const &	k,
		Real const &	lambda
	)

static

Returns: a pseudo Weibull random variate with the specified parameters.

Parameters

k,lambda shape and scale (dispersion) parameters

Definition at line 88 of file STK_Law_Weibull.cpp.

{
  return 0;
}

◆ setK()

void STK::Law::Weibull::setK ( Real const & k )

inline

Parameters

k	set the shape parameter

Definition at line 77 of file STK_Law_Weibull.h.

    {
      if (k<=0) STKDOMAIN_ERROR_1ARG(Weibull::setShape,k,shape must be > 0);
      k_ = k;
    }

References k(), k_, and STKDOMAIN_ERROR_1ARG.

◆ setLambda()

void STK::Law::Weibull::setLambda ( Real const & lambda )

inline

Parameters

lambda set the scale parameter

Definition at line 83 of file STK_Law_Weibull.h.

    {
      if (lambda<=0) STKDOMAIN_ERROR_1ARG(Weibull::setScale,lambda,scale must be > 0);
      lambda_ = lambda;
    }

References lambda(), lambda_, and STKDOMAIN_ERROR_1ARG.

Member Data Documentation

◆ k_

Real STK::Law::Weibull::k_

protected

The shape parameter.

Definition at line 149 of file STK_Law_Weibull.h.

Referenced by k(), and setK().

◆ lambda_

Real STK::Law::Weibull::lambda_

protected

The scale parameter.

Definition at line 151 of file STK_Law_Weibull.h.

Referenced by lambda(), and setLambda().

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

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Base

Constructor & Destructor Documentation

◆ Weibull()

◆ ~Weibull()

Member Function Documentation

◆ cdf() [1/2]

◆ cdf() [2/2]

◆ icdf() [1/2]

◆ icdf() [2/2]

◆ k()

◆ lambda()

◆ lpdf() [1/2]

◆ lpdf() [2/2]

◆ pdf() [1/2]

◆ pdf() [2/2]

◆ rand() [1/2]

◆ rand() [2/2]

◆ setK()

◆ setLambda()

Member Data Documentation

◆ k_

◆ lambda_