akki - 3 months ago 15

C++ Question

I am trying to generate high quality random numbers in the range (0,1) in my project and I tried testing the

`uniform_real_distribution`

`#include <random>`

#include <iostream>

#include <chrono>

using namespace std;

// obtain a seed from the system clock:

unsigned seed = static_cast<int> (chrono::system_clock::now().time_since_epoch().count());

// globally defining the generator and making it static for safety because in the

// actual project this might affect the flow.

static default_random_engine gen(seed);

uniform_real_distribution<double> distribution(0.0,1.0);

int main(){

const int nrolls=10000; // number of experiments

const int nstars=95; // maximum number of stars to distribute

const int nintervals=10; // number of intervals

int p[nintervals]={};

for (int i=0; i<nrolls; ++i) {

double number = distribution(gen);

++p[int(nintervals*number)];

}

std::cout << "uniform_real_distribution (0.0,1.0):" << std::endl;

std::cout << std::fixed; std::cout.precision(1);

for (int i=0; i<nintervals; ++i) {

std::cout << float(i)/nintervals << "-" << float(i+1)/nintervals << ": ";

std::cout << std::string(p[i]*nstars/nrolls,'*') << std::endl;

}

return 0;

}

The random numbers were not uniformly distributed. The output of the same when executed repeatedly is:

F:\path>randtest

uniform_real_distribution (0.0,1.0):

0.0-0.1: *********

0.1-0.2: **********

0.2-0.3: ********

0.3-0.4: *********

0.4-0.5: *********

0.5-0.6: *********

0.6-0.7: *********

0.7-0.8: *********

0.8-0.9: *********

0.9-1.0: **********

F:\path>randtest

uniform_real_distribution (0.0,1.0):

0.0-0.1: *********

0.1-0.2: *********

0.2-0.3: *********

0.3-0.4: *********

0.4-0.5: *********

0.5-0.6: *********

0.6-0.7: *********

0.7-0.8: *********

0.8-0.9: *********

0.9-1.0: *********

F:\path>randtest

uniform_real_distribution (0.0,1.0):

0.0-0.1: *********

0.1-0.2: *********

0.2-0.3: *********

0.3-0.4: *********

0.4-0.5: **********

0.5-0.6: *********

0.6-0.7: *********

0.7-0.8: *********

0.8-0.9: *********

0.9-1.0: *********

Is it because of the seeding? or is it better to use a different generator?

I use G++ 5.1.0 compiler c++11 standards.

Answer

If you flipped a coin once and it landed heads, would it always land on tails the next time you flipped it?

A coin produces a uniform distribution on the set `{heads, tails}`

. That doesn't mean for any set of flips, the number of heads and tails is equal. In fact, the chance of that happening *exactly* goes *down* as you flip more coins.

In your case, each of those intervals have a 10% chance of being selected.

The variance of such a selection is (0.1)(1-.1), or 0.09.

The expected value is 0.1.

After 10000 attempts, the expected value is going to be 1000.

Tha variance is going to be 900.

900 variance corresponds to a standard deviation of 30.

The 95-ish% confidence interval is 2 standard deviations (actually 1.96, but who cares).

So you should expect the values to typically be between 940 and 1060.

With 95 stars, each star corresponds to 10000/95=105 elements.

940/105 is approx 8.95 1060/105 is approx 10.06

So you'll usually see between 8 and 10 stars on each column. Assuming rounding down, hitting 7 or 11 stars should be very rare (as that is 3 SD away) even on 10 anti-correlated samples.

This all assumes a perfect uniform random distribution. As this models your observed behavior, your problem is with mathematics and the definition of uniform *random* distribution, not the C++ language.

If you want a perfect histogram, don't use a uniform random distribution. For example, you could simply start with 0, then add 0.0001 each time. After 10001 calls you'll have a uniform histogram from 0 to 1.

Uniform random simply means the chance of each region is the same.