26 Numerics library [numerics]

26.5 Random number generation [rand]

26.5.8 Random number distribution class templates [rand.dist]

26.5.8.5 Normal distributions [rand.dist.norm]

26.5.8.5.1 Class template normal_distribution [rand.dist.norm.normal]

1

A normal_distribution random number distribution produces random numbers x distributed according to the probability density function \[% p(x\,|\,\mu,\sigma) = {1 \over \sigma \sqrt{2\pi}} \cdot % e^{-(x-\mu)^2 / (2\sigma^2)} \exp{\left(- \, \frac{(x - \mu)^2} {2 \sigma^2} \right) } \; \mbox{.} \] The distribution parameters μ and σ are also known as this distribution's mean and standard deviation.

template<class RealType = double>
 class normal_distribution{
public:
 // types
 typedef RealType result_type;
 typedef unspecified param_type;

 // constructors and reset functions
 explicit normal_distribution(RealType mean = 0.0, RealType stddev = 1.0);
 explicit normal_distribution(const param_type& parm);
 void reset();

 // generating functions
 template<class URNG>
   result_type operator()(URNG& g);
 template<class URNG>
   result_type operator()(URNG& g, const param_type& parm);

 // property functions
 RealType mean() const;
 RealType stddev() const;
 param_type param() const;
 void param(const param_type& parm);
 result_type min() const;
 result_type max() const;
};

explicit normal_distribution(RealType mean = 0.0, RealType stddev = 1.0);

2

Requires: 0 < stddev .

3

Effects: Constructs a normal_distribution object; mean and stddev correspond to the respective parameters of the distribution.

RealType mean() const;

4

Returns: The value of the mean parameter with which the object was constructed.

RealType stddev() const;

5

Returns: The value of the stddev parameter with which the object was constructed.

26.5.8.5.2 Class template lognormal_distribution [rand.dist.norm.lognormal]

1

A lognormal_distribution random number distribution produces random numbers x > 0 distributed according to the probability density function \[% p(x\,|\,m,s) = \frac{1} {s x \sqrt{2 \pi}} \cdot \exp{\left(- \, \frac{(\ln{x} - m)^2} {2 s^2} \right) } \; \mbox{.} \]

template<class RealType = double>
 class lognormal_distribution{
public:
 // types
 typedef RealType result_type;
 typedef unspecified param_type;

 // constructor and reset functions
 explicit lognormal_distribution(RealType m = 0.0, RealType s = 1.0);
 explicit lognormal_distribution(const param_type& parm);
 void reset();

 // generating functions
 template<class URNG>
   result_type operator()(URNG& g);
 template<class URNG>
   result_type operator()(URNG& g, const param_type& parm);

 // property functions
 RealType m() const;
 RealType s() const;
 param_type param() const;
 void param(const param_type& parm);
 result_type min() const;
 result_type max() const;
};

explicit lognormal_distribution(RealType m = 0.0, RealType s = 1.0);

2

Requires: 0 < s .

3

Effects: Constructs a lognormal_distribution object; m and s correspond to the respective parameters of the distribution.

RealType m() const;

4

Returns: The value of the m parameter with which the object was constructed.

RealType s() const;

5

Returns: The value of the s parameter with which the object was constructed.

26.5.8.5.3 Class template chi_squared_distribution [rand.dist.norm.chisq]

1

A chi_squared_distribution random number distribution produces random numbers x>0 distributed according to the probability density function \[% p(x\,|\,n) = \frac{ x^{(n/2)-1} \cdot e^{-x/2}} {\Gamma(n/2) \cdot 2^{n/2}} \; \mbox{.} \]

template<class RealType = double>
 class chi_squared_distribution{
public:
 // types
 typedef RealType result_type;
 typedef unspecified param_type;

 // constructor and reset functions
 explicit chi_squared_distribution(RealType n = 1);
 explicit chi_squared_distribution(const param_type& parm);
 void reset();

 // generating functions
 template<class URNG>
   result_type operator()(URNG& g);
 template<class URNG>
   result_type operator()(URNG& g, const param_type& parm);

 // property functions
 RealType n() const;
 param_type param() const;
 void param(const param_type& parm);
 result_type min() const;
 result_type max() const;
};

explicit chi_squared_distribution(RealType n = 1);

2

Requires: 0 < n .

3

Effects: Constructs a chi_squared_distribution object; n corresponds to the parameter of the distribution.

RealType n() const;

4

Returns: The value of the n parameter with which the object was constructed.

26.5.8.5.4 Class template cauchy_distribution [rand.dist.norm.cauchy]

1

A cauchy_distribution random number distribution produces random numbers x distributed according to the probability density function \[% p(x\,|\,a,b) = \left( \pi b \left( 1 + \left( \frac{x-a}{b} \right)^2 \;\right)\right)^{-1} \; \mbox{.} \]

template<class RealType = double>
 class cauchy_distribution{
public:
 // types
 typedef RealType result_type;
 typedef unspecified param_type;

 // constructor and reset functions
 explicit cauchy_distribution(RealType a = 0.0, RealType b = 1.0);
 explicit cauchy_distribution(const param_type& parm);
 void reset();

 // generating functions
 template<class URNG>
   result_type operator()(URNG& g);
 template<class URNG>
   result_type operator()(URNG& g, const param_type& parm);

 // property functions
 RealType a() const;
 RealType b() const;
 param_type param() const;
 void param(const param_type& parm);
 result_type min() const;
 result_type max() const;
};

explicit cauchy_distribution(RealType a = 0.0, RealType b = 1.0);

2

Requires: 0 < b .

3

Effects: Constructs a cauchy_distribution object; a and b correspond to the respective parameters of the distribution.

RealType a() const;

4

Returns: The value of the a parameter with which the object was constructed.

RealType b() const;

5

Returns: The value of the b parameter with which the object was constructed.

26.5.8.5.5 Class template fisher_f_distribution [rand.dist.norm.f]

1

A fisher_f_distribution random number distribution produces random numbers x≥0 distributed according to the probability density function \[% p(x\,|\,m,n) = \frac{\Gamma\big((m+n)/2\big)} {\Gamma(m/2) \; \Gamma(n/2)} \cdot \left(\frac{m}{n}\right)^{m/2} \cdot x^{(m/2)-1} \cdot {\left( 1 + \frac{m x}{n} \right)}^{-(m+n)/2} \; \mbox{.} \]

template<class RealType = double>
 class fisher_f_distribution{
public:
 // types
 typedef RealType result_type;
 typedef unspecified param_type;

 // constructor and reset functions
 explicit fisher_f_distribution(RealType m = 1, RealType n = 1);
 explicit fisher_f_distribution(const param_type& parm);
 void reset();

 // generating functions
 template<class URNG>
   result_type operator()(URNG& g);
 template<class URNG>
   result_type operator()(URNG& g, const param_type& parm);

 // property functions
 RealType m() const;
 RealType n() const;
 param_type param() const;
 void param(const param_type& parm);
 result_type min() const;
 result_type max() const;
};

explicit fisher_f_distribution(RealType m = 1, RealType n = 1);

2

Requires: 0 < m and 0 < n .

3

Effects: Constructs a fisher_f_distribution object; m and n correspond to the respective parameters of the distribution.

RealType m() const;

4

Returns: The value of the m parameter with which the object was constructed.

RealType n() const;

5

Returns: The value of the n parameter with which the object was constructed.

26.5.8.5.6 Class template student_t_distribution [rand.dist.norm.t]

1

A student_t_distribution random number distribution produces random numbers x distributed according to the probability density function \[% p(x\,|\,n) = \frac{1} {\sqrt{n \pi}} \cdot \frac{\Gamma\big((n+1)/2\big)} {\Gamma(n/2)} \cdot \left( 1+\frac{x^2}{n} \right) ^ {-(n+1)/2} \; \mbox{.} \]

template<class RealType = double>
 class student_t_distribution{
public:
 // types
 typedef RealType result_type;
 typedef unspecified param_type;

 // constructor and reset functions
 explicit student_t_distribution(RealType n = 1);
 explicit student_t_distribution(const param_type& parm);
 void reset();

 // generating functions
 template<class URNG>
   result_type operator()(URNG& g);
 template<class URNG>
   result_type operator()(URNG& g, const param_type& parm);

 // property functions
 RealType n() const;
 param_type param() const;
 void param(const param_type& parm);
 result_type min() const;
 result_type max() const;
};

explicit student_t_distribution(RealType n = 1);

2

Requires: 0 < n .

3

Effects: Constructs a student_t_distribution object; n corresponds to the parameter of the distribution.

RealType n() const;

4

Returns: The value of the n parameter with which the object was constructed.