NegativeBinomial probability law. More...

#include <STK_Law_NegativeBinomial.h>

Inheritance diagram for STK::Law::NegativeBinomial:

Public Types
typedef IUnivLaw< Integer >	Base

Public Member Functions
	NegativeBinomial (int size=1, Real const &prob=0.5)
	constructor

virtual	~NegativeBinomial ()
	destructor

Real const &	prob () const

int	size () const

void	setProb (Real const &prob)

void	setSize (Integer size)

virtual Integer	rand () const

virtual Real	cdf (Real const &t) const
	compute the cumulative distribution function Give the probability that a NegativeBinomial random variate is less or equal to t.

virtual Real	pdf (Integer const &x) const
	compute the probability distribution function (density) Give the value of the pdf at the point x.

virtual Real	lpdf (Integer const &x) const
	compute the log probability distribution function Give the value of the log-pdf at the point x.

virtual Integer	icdf (Real const &p) const
	inverse cumulative distribution function The quantile is defined as the smallest value x such that F(x) >= p , where F is the cumulative distribution function.

Public Member Functions inherited from STK::Law::IUnivLaw< Integer >
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 Integer	rand (int size, Real const &prob)

static Real	pdf (Integer x, int size, Real const &prob)
	compute the probability distribution function (density) Give the value of the pdf at the point x.

static Real	lpdf (Integer x, int size, Real const &prob)
	compute the log probability distribution function Give the value of the log-pdf at the point x.

static Real	cdf (Real const &t, int size, Real const &prob)
	compute the cumulative distribution function Give the value of the cdf at the point t.

static Integer	icdf (Real const &p, int size, Real const &prob)
	inverse cumulative distribution function The quantile is defined as the smallest value x such that F(x) >= p , where F is the cumulative distribution function.

Protected Attributes
int	size_
	number of successes

Real	prob_
	probability of success in a Bernoulli trial

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

Additional Inherited Members
Protected Member Functions inherited from STK::Law::IUnivLaw< Integer >
	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

NegativeBinomial probability law.

In probability theory and statistics, the negative binomial distribution is a discrete probability distribution of the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures (denoted r) occurs.

Suppose there is a sequence of independent Bernoulli trials, each trial having two potential outcomes called “success” and “failure”. In each trial the probability of success is p and of failure is (1 − p). We are observing this sequence until a predefined number r of failures has occurred. Then the random number of successes we have seen, X, will have the negative binomial (or Pascal) distribution: $X\ \sim\ \text{NB}(r; p)$

The probability mass function of the negative binomial distribution is

$f(k; r, p) = \Pr(X = k) = \binom{k+r-1}{k} p^k(1-p)^r \quad\text{for } k = 0, 1, 2, \dots$

Definition at line 68 of file STK_Law_NegativeBinomial.h.

Member Typedef Documentation

◆ Base

typedef IUnivLaw<Integer> STK::Law::NegativeBinomial::Base

Definition at line 71 of file STK_Law_NegativeBinomial.h.

Constructor & Destructor Documentation

◆ NegativeBinomial()

STK::Law::NegativeBinomial::NegativeBinomial	(	int	size = `1`,
		Real const &	prob = `0.5`
	)

inline

constructor

Parameters

prob,size probability of success and number of successes in a NegativeBinomial trial

Definition at line 75 of file STK_Law_NegativeBinomial.h.

76 : Base(_T("Negative Binomial")), size_(size), prob_(prob) {}

_T

#define _T(x)

Let x unmodified.

Definition STK_Typedefs.h:71

STK::Law::NegativeBinomial::prob

Real const & prob() const

Definition STK_Law_NegativeBinomial.h:81

STK::Law::NegativeBinomial::size_

int size_

number of successes

Definition STK_Law_NegativeBinomial.h:170

STK::Law::NegativeBinomial::Base

IUnivLaw< Integer > Base

Definition STK_Law_NegativeBinomial.h:71

STK::Law::NegativeBinomial::size

int size() const

Definition STK_Law_NegativeBinomial.h:83

STK::Law::NegativeBinomial::prob_

Real prob_

probability of success in a Bernoulli trial

Definition STK_Law_NegativeBinomial.h:172

◆ ~NegativeBinomial()

virtual STK::Law::NegativeBinomial::~NegativeBinomial ( )

inlinevirtual

destructor

Definition at line 79 of file STK_Law_NegativeBinomial.h.

79{}

Member Function Documentation

◆ cdf() [1/2]

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

virtual

compute the cumulative distribution function Give the probability that a NegativeBinomial random variate is less or equal to t.

Parameters

t	a real value

Returns: the value of the cdf

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

Definition at line 76 of file STK_Law_NegativeBinomial.cpp.

{
  return 0;
}

◆ cdf() [2/2]

Real STK::Law::NegativeBinomial::cdf	(	Real const &	t,
		int	size,
		Real const &	prob
	)

static

compute the cumulative distribution function Give the value of the cdf at the point t.

Parameters

t	a real value
size,prob	probability of success and number of successes in a NegativeBinomial trial

Returns: the value of the cdf

Definition at line 123 of file STK_Law_NegativeBinomial.cpp.

{
  return 0;
}

◆ icdf() [1/2]

Integer STK::Law::NegativeBinomial::icdf ( Real const & p ) const

virtual

inverse cumulative distribution function The quantile is defined as the smallest value x such that F(x) >= p , where F is the cumulative distribution function.

Parameters

p	a probability number

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

Definition at line 85 of file STK_Law_NegativeBinomial.cpp.

{
  return 0;
}

◆ icdf() [2/2]

Integer STK::Law::NegativeBinomial::icdf	(	Real const &	p,
		int	size,
		Real const &	prob
	)

static

inverse cumulative distribution function The quantile is defined as the smallest value x such that F(x) >= p , where F is the cumulative distribution function.

Parameters

p	a probability number
prob,size	probability of success and number of successes in a NegativeBinomial trial

Definition at line 132 of file STK_Law_NegativeBinomial.cpp.

{
  return 0;
}

◆ lpdf() [1/2]

Real STK::Law::NegativeBinomial::lpdf ( Integer const & x ) const

virtual

compute the log probability distribution function Give the value of the log-pdf at the point x.

Parameters

x	a binary value

Returns: the value of the log-pdf

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

Definition at line 66 of file STK_Law_NegativeBinomial.cpp.

{
  return 0;
}

◆ lpdf() [2/2]

Real STK::Law::NegativeBinomial::lpdf	(	Integer	x,
		int	size,
		Real const &	prob
	)

static

compute the log probability distribution function Give the value of the log-pdf at the point x.

Parameters

x	an integer value
prob,size	probability of success and number of successes in a NegativeBinomial trial

Returns: the value of the log-pdf

Definition at line 113 of file STK_Law_NegativeBinomial.cpp.

{
  return 0;
}

◆ pdf() [1/2]

Real STK::Law::NegativeBinomial::pdf ( Integer const & x ) const

virtual

compute the probability distribution function (density) Give the value of the pdf at the point x.

Parameters

x	a binary value

Returns: the value of the pdf

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

Definition at line 57 of file STK_Law_NegativeBinomial.cpp.

{
  return 0;
}

◆ pdf() [2/2]

Real STK::Law::NegativeBinomial::pdf	(	Integer	x,
		int	size,
		Real const &	prob
	)

static

compute the probability distribution function (density) Give the value of the pdf at the point x.

Parameters

x	an integer value
prob,size	probability of success and number of successes in a NegativeBinomial trial

Returns: the value of the pdf

Definition at line 103 of file STK_Law_NegativeBinomial.cpp.

{
  return 0;
}

◆ prob()

Real const & STK::Law::NegativeBinomial::prob ( ) const

inline

Returns: the probability of success

Definition at line 81 of file STK_Law_NegativeBinomial.h.

81{ return prob_;}

References prob_.

Referenced by setProb().

◆ rand() [1/2]

Integer STK::Law::NegativeBinomial::rand ( ) const

virtual

Returns: a Integer random variate .

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

Definition at line 48 of file STK_Law_NegativeBinomial.cpp.

{
  return 0;
}

◆ rand() [2/2]

Integer STK::Law::NegativeBinomial::rand	(	int	size,
		Real const &	prob
	)

static

Parameters

prob,size probability of success and number of successes in a NegativeBinomial trial

Returns: a Integer random variate.

Definition at line 93 of file STK_Law_NegativeBinomial.cpp.

{
  return 0;
}

◆ setProb()

void STK::Law::NegativeBinomial::setProb ( Real const & prob )

inline

Parameters

prob	the probability of success to set

Definition at line 85 of file STK_Law_NegativeBinomial.h.

    {
      if (prob<0) STKDOMAIN_ERROR_1ARG(NegativeBinomial::setProb,prob,prob must be >= 0);
      if (prob>1) STKDOMAIN_ERROR_1ARG(NegativeBinomial::setProb,prob,prob must be <= 1);
      prob_ = prob;
    }

References prob(), prob_, setProb(), and STKDOMAIN_ERROR_1ARG.

Referenced by setProb().

◆ setSize()

void STK::Law::NegativeBinomial::setSize ( Integer size )

inline

Parameters

size	the number of successes to set

Definition at line 92 of file STK_Law_NegativeBinomial.h.

    {
      if (size<0) STKDOMAIN_ERROR_1ARG(NegativeBinomial::setSize,size,size must be >= 0);
      size_ = size;
    }

References setSize(), size(), size_, and STKDOMAIN_ERROR_1ARG.

Referenced by setSize().

◆ size()

int STK::Law::NegativeBinomial::size ( ) const

inline

Returns: the number of trials

Definition at line 83 of file STK_Law_NegativeBinomial.h.

83{ return size_;}

References size_.

Referenced by setSize().

Member Data Documentation

◆ prob_

Real STK::Law::NegativeBinomial::prob_

protected

probability of success in a Bernoulli trial

Definition at line 172 of file STK_Law_NegativeBinomial.h.

Referenced by prob(), and setProb().

◆ size_

int STK::Law::NegativeBinomial::size_

protected

number of successes

Definition at line 170 of file STK_Law_NegativeBinomial.h.

Referenced by setSize(), and size().

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

◆ NegativeBinomial()

◆ ~NegativeBinomial()

Member Function Documentation

◆ cdf() [1/2]

◆ cdf() [2/2]

◆ icdf() [1/2]

◆ icdf() [2/2]

◆ lpdf() [1/2]

◆ lpdf() [2/2]

◆ pdf() [1/2]

◆ pdf() [2/2]

◆ prob()

◆ rand() [1/2]

◆ rand() [2/2]

◆ setProb()

◆ setSize()

◆ size()

Member Data Documentation

◆ prob_

◆ size_