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Difference between revisions of "cpp/numeric/random/lognormal distribution"

From cppreference.com
< cpp‎ | numeric‎ | random
m (Use since= and until= params of {{ddcl}} template.)
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{{cpp/title|lognormal_distribution}}
 
{{cpp/title|lognormal_distribution}}
 
{{cpp/numeric/random/lognormal_distribution/navbar}}
 
{{cpp/numeric/random/lognormal_distribution/navbar}}
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{{ddcl | header=random | since=c++11 | 1=
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{{ddcl|header=random|since=c++11|1=
 
template< class RealType = double >
 
template< class RealType = double >
 
class lognormal_distribution;
 
class lognormal_distribution;
 
}}
 
}}
  
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The lognormal_distribution random number distribution produces random numbers {{math|x > 0}} according to a log-normal distribution:
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The lognormal_distribution random number distribution produces random numbers {{math|x > 0}} according to a -normal distribution:
  
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:{{math|f(x; m,s) {{=}} {{mfrac||1|sx{{mrad|2 π}} }} exp{{mparen|(|)|- {{mfrac||(ln x - m){{su|p=2}}| 2s{{su|p=2}}}} }} }}
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:{{|f(x;m,s) {{} } {{mfrac||1|sx{{mrad|2 π}}}} exp{{mparen|(|)|- {{mfrac||(ln x - m){{su|p=2}}|2s{{su|p=2}}}}}}}}
  
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The parameter {{math|m}} is the mean and the parameter {{math|s}} the standard deviation.
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The {{math|m}} and {{math|s}} the standard deviation .
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===Member types===
 
===Member types===
 
{{dsc begin}}
 
{{dsc begin}}
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{{dsc hitem | Member type | Definition}}
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{{dsc hitem|Member type|Definition}}
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{{dsc | {{tt|result_type}} | {{c|RealType}}}}
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{{dsc|{{tt|result_type}} {{c|RealType}}}}
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{{dsc | {{tt|param_type}} | the type of the parameter set, unspecified}}
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{{param_type}}
 
{{dsc end}}
 
{{dsc end}}
  
 
===Member functions===
 
===Member functions===
 
{{dsc begin}}
 
{{dsc begin}}
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{{dsc inc | cpp/numeric/random/distribution/dsc constructor | lognormal_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc constructor|lognormal_distribution}}
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{{dsc inc | cpp/numeric/random/distribution/dsc reset | lognormal_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc reset|lognormal_distribution}}
  
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{{dsc h2 | Generation}}
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{{dsc h2|Generation}}
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{{dsc inc | cpp/numeric/random/distribution/dsc operator() | lognormal_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc operator()|lognormal_distribution}}
  
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{{dsc h2 | Characteristics}}
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{{dsc h2|Characteristics}}
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{{dsc inc | cpp/numeric/random/distribution/dsc params | lognormal_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc params|lognormal_distribution}}
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{{dsc inc | cpp/numeric/random/distribution/dsc param | lognormal_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc param|lognormal_distribution}}
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{{dsc inc | cpp/numeric/random/distribution/dsc min | lognormal_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc min|lognormal_distribution}}
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{{dsc inc | cpp/numeric/random/distribution/dsc max | lognormal_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc max|lognormal_distribution}}
 
{{dsc end}}
 
{{dsc end}}
  
 
===Non-member functions===
 
===Non-member functions===
 
{{dsc begin}}
 
{{dsc begin}}
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{{dsc inc | cpp/numeric/random/distribution/dsc operator_cmp | lognormal_distribution }}
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{{dsc inc|cpp/numeric/random/distribution/dsc operator_cmp|lognormal_distribution}}
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{{dsc inc | cpp/numeric/random/distribution/dsc operator_ltltgtgt | lognormal_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc operator_ltltgtgt|lognormal_distribution}}
 
{{dsc end}}
 
{{dsc end}}
  
 
===Example===
 
===Example===
 
{{example
 
{{example
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| code=
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|code=
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#include <iostream>
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#include <>
 
#include <iomanip>
 
#include <iomanip>
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#include <string>
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#include <>
 
#include <map>
 
#include <map>
 
#include <random>
 
#include <random>
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#include <cmath>
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#include <>
 +
 
 
int main()
 
int main()
 
{
 
{
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     std::map<int, int> hist;
 
     std::map<int, int> hist;
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     for(int n=0; n<10000; ++n) {
+
     for (int n = 0; n < ; ++n)
 
         ++hist[std::round(d(gen))];
 
         ++hist[std::round(d(gen))];
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    }
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     for(auto p : hist) {
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     for (std::cout << std::fixed << std::setprecision(1)
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        std::cout << std::fixed << std::setprecision(1) << std::setw(2)
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<< std::<< << ' ' << std::string(/ 200, '*') << '\n';
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                  << p.first << ' ' << std::string(p.second/200, '*') << '\n';
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−
    }
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}
 
}
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| output=
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2  
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|output=
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3 ***
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2
−
4 *************
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3 ***
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5 ***************
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4 *************
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6 *********
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5 ***************
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7 ****
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6 *********
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8 *
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7 ****
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9  
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8 *
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10
+
9
−
11
+
−
12
+
 +
 
}}
 
}}
  
 
===External links===
 
===External links===
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* [http://mathworld.wolfram.com/LogNormalDistribution.html Weisstein, Eric W. "Log Normal Distribution."] From MathWorld--A Wolfram Web Resource.
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[://mathworld.wolfram.com/LogNormalDistribution.html Weisstein, Eric W. "Log Normal Distribution."] From MathWorld A Wolfram Web Resource.
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* [https://en.wikipedia.org/wiki/Log-normal_distribution Log-normal distribution.] From Wikipedia.
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Latest revision as of 06:21, 2 May 2023

 
C++
 
Numerics library
 
Pseudo-random number generation
 
std::lognormal_distribution
 
Defined in header <random>
template< class RealType = double >
class lognormal_distribution;
 (since C++11)

The lognormal_distribution random number distribution produces random numbers x > 0 according to a Log-normal distribution:

f(x; m,s) =
1
sx√2 π
 exp⎛
⎜
⎝-
(ln x - m)2
2s2
⎞
⎟
⎠

The parameters m and s are, respectively, the mean and standard deviation of the natural logarithm of x.

std::lognormal_distribution satisfies all requirements of RandomNumberDistribution.

Contents

[edit] Template parameters

RealType - The result type generated by the generator. The effect is undefined if this is not one of float, double, or long double.

[edit] Member types

Member type Definition
result_type (C++11) RealType
param_type (C++11) the type of the parameter set, see RandomNumberDistribution.

[edit] Member functions

(C++11)
 constructs new distribution
(public member function) [edit]
(C++11)
 resets the internal state of the distribution
(public member function) [edit]
Generation
(C++11)
 generates the next random number in the distribution
(public member function) [edit]
Characteristics
(C++11)
 returns the distribution parameters
(public member function) [edit]
(C++11)
 gets or sets the distribution parameter object
(public member function) [edit]
(C++11)
 returns the minimum potentially generated value
(public member function) [edit]
(C++11)
 returns the maximum potentially generated value
(public member function) [edit]

[edit] Non-member functions

(C++11)(C++11)(removed in C++20)
 compares two distribution objects
(function) [edit]
(C++11)
 performs stream input and output on pseudo-random number distribution
(function template) [edit]

[edit] Example

Run this code
#include <cmath>
#include <iomanip>
#include <iostream>
#include <map>
#include <random>
#include <string>
 
int main()
{
    std::random_device rd;
    std::mt19937 gen(rd());
 
    std::lognormal_distribution<> d(1.6, 0.25);
 
    std::map<int, int> hist;
    for (int n = 0; n < 1e4; ++n)
        ++hist[std::round(d(gen))];
 
    for (std::cout << std::fixed << std::setprecision(1); auto [x, y] : hist)
        std::cout << std::hex << x << ' ' << std::string(y / 200, '*') << '\n';
}

Possible output: 

2
3 ***
4 *************
5 ***************
6 *********
7 ****
8 *
9
a
b
c

[edit] External links

Weisstein, Eric W. "Log Normal Distribution." From MathWorld — A Wolfram Web Resource.
Retrieved from "https://en.cppreference.com/mwiki/index.php?title=cpp/numeric/random/lognormal_distribution&oldid=151295"