# Random Sample

Generates random numbers following a Chi-Square distribution.

Controller: **CodeCogs**

## Dependents

## Interface

C++

Excel

## Class RandomSample

The chi-square distribution is a univariate distribution which results when univariate-normal variables are squared, and possibly summed. While the normal distribution is symmetric, the chi-square distribution is skewed to the right, and has a minimum of 0. The degrees of freedom of the resulting chi-square distribution are equal to the number of variables that are summed. The mean of a chi-square distribution is equal to its degrees of freedom, and the variance is equal to twice the degrees of freedom. These chi-square distributions are themselves additive. That is, a chi-square-distributed variable with degrees of freedom can be added to one with degrees of freedom to yield a chi-square-distributed variable with degrees of freedom, as long as the two added variables are independent. Analogous results can be obtained by subtraction, under the same condition. The probability density function for the chi-square distribution with degrees of freedom is given by If some or all of the original normal variables had nonzero mean, then the result will be a noncentral chi-square distribution, with noncentrality parameter . The effect of the noncentrality parameter is to move the distribution to the right and to make it appear flatter and more symmetrical. Adding two independent noncentral chi-square distributed variables with noncentrality parameters and yields a noncentral chi-square distributed variable with noncentrality parameter . Using this class, the diagram below is generated from two distinct sequences of 1000 random numbers. Each pair of numbers are plotted against each other, to illustrate the Chi-Square behaviour of this non-uniform random number generator.## Speed:

The average running time for generating 100,000,000 random numbers using this class on a 750MHz microprocessor is 76 seconds.## References:

- Ed Rigdon's structural equation modeling FAQ, http://www2.gsu.edu/~mkteer/semfaq.html
- MathWorld, http://mathworld.wolfram.com/Chi-SquaredDistribution.html
- The Newran03 random number generator library of Robert Davies, http://www.robertnz.net/nr03doc.htm

### Example 1

- The following example displays 40 random floating point numbers from a chi-square distribution.
It uses two different generators to achieve this. The first generator uses a particular value
to initialize the seed, while the second one is using the system timer. Notice that it was necessary
to divide the timer with the MERSENNEDIV value in order to keep the seed in the (0, 1) interval.
Since the seed of the first generator is never changed, the first 20 numbers will always
remain the same. However since the second generator is initialized via the system timer,
the next 20 numbers will obviously vary with each execution of the program,
#include <iostream> #include <time.h> #include <codecogs/stats/dists/continuous/chisquared/randomsample.h> using namespace std; int main() { Stats::Dists::Continuous::ChiSquared::RandomSample A(10, 12.57, 0.813); Stats::Dists::Continuous::ChiSquared::RandomSample B(13, 11.06, time(0) / MERSENNEDIV); for (int i = 0; i < 20; ++i) cout << A.genReal() << endl; cout << endl; for (int i = 0; i < 20; ++i) cout << B.genReal() << endl; return 0; }

Below you will find 20 numbers corresponding to the output of the first generator :13.1348 34.8509 29.1836 21.0783 20.1372 20.8733 16.2834 26.6546 26.4716 30.2577 38.5005 21.1584 23.6544 24.2537 25.5915 14.5727 14.215 16.0628 25.3528 18.4918

### Authors

*Lucian Bentea*

##### Source Code

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## Unknown

RandomSample::RandomSampleunknown( | int | df | |

double | noncen | ||

double | s | ) |

### Parameters

s random number seed

##### Source Code

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## Sample

doublesample( | int | df | |

double | noncen | ||

double | seed` = 0` | ) |

#include <time.h> ... sample(df, noncen, time(0) / MERSENNEDIV);If you require more advance behaviour, we strongly recommend that directly use the underlying class randomsample that is provided with this module.

Graph is not currently available

### Parameters

df degree of freedom seed sets the initial seed for the random generator. Only used in the first call to this function

##### Source Code

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