cppdraft_translate/cppdraft/rand/dist/norm/cauchy.md

[rand.dist.norm.cauchy]

29 Numerics library [numerics]

29.5 Random number generation [rand]

29.5.9 Random number distribution class templates [rand.dist]

29.5.9.5 Normal distributions [rand.dist.norm]

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

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A cauchy_distribution random number distribution produces random numbers x distributed according to the probability density function in Formula 29.16.

p(x|a,b)=(πb(1+(x−ab)2))−1(29.16)

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namespace std {templateclass cauchy_distribution {public:// typesusing result_type = RealType; using param_type = unspecified; // constructor and reset functions cauchy_distribution() : cauchy_distribution(0.0) {}explicit cauchy_distribution(RealType a, RealType b = 1.0); explicit cauchy_distribution(const param_type& parm); void reset(); // equality operatorsfriend bool operator==(const cauchy_distribution& x, const cauchy_distribution& y); // generating functionstemplate result_type operator()(URBG& g); template result_type operator()(URBG& 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; // inserters and extractorstemplate<class charT, class traits>friend basic_ostream<charT, traits>&operator<<(basic_ostream<charT, traits>& os, const cauchy_distribution& x); template<class charT, class traits>friend basic_istream<charT, traits>&operator>>(basic_istream<charT, traits>& is, cauchy_distribution& x); };}

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

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Preconditions: 0<b.

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Remarks: a and b correspond to the respective parameters of the distribution.

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RealType a() const;

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

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RealType b() const;

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