Need a normally-distributed random number generator

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I am new to C++ but have a background in mathematics. I am trying to create a random number generator that will spit out a decimal (dollar amount) between 1.00 and 2.00 with an approximately normal distribution (so that the mean is 1.50).

Now, I have never tried anything like this and have not found a similar question that specifically spits out an element from a set of numbers with normally distributed probabilities. In this model, 1.50 would be most likely to come up, 1.00 or 2.00 would have almost no chance of appearing.

It's easy enough to write a p.d.f. for a normal distribution with mean=1.50 and 3*sigma = 0.5 --> sigma = 1/6 (so that nearly all data is between 1.00 and 2.00). However, more than just not knowing how to integrate 101 regions under this curve (which I dont think can be solved analytically) with C++, it doesn't sound efficient to me. I know there is a normal distribution function in C++.

Can somebody please help me write this out, with comments? Thank you

The C++ standard library has a normal distribution class - just what you've asked for. Use it - and clip the value so it's between your minimum and maximum:

#include <algorithm> // for std::clamp()
#include <iostream>
#include <random>

int main() {
    std::random_device randomness_device{};
    std::mt19937 pseudorandom_generator{randomness_device()};

    auto mean = 1.5;
    auto std_dev = 0.5;
    auto min_allowed = 1.0;
    auto max_allowed = 2.0;
    std::normal_distribution<> distribution{mean, std_dev};
    auto sample = distribution(pseudorandom_generator);
    auto clamped = 
        // C++17 and later
        std::clamp(sample, min_allowed, max_allowed);
        // C++14 or earlier:
        // std::max(min_allowed,std::min(sample, max_allowed));

        << "A value from a normal distribution with mean " << mean
        << " and standard deviation " << std_dev << ": "   << sample
        << "; when clamped to [" << min_allowed << ", " 
        << max_allowed << "], we get: " << clamped << "\n";

In terms of the distribution - this changes the measure so that the entire range (-infinity,1) is concentrated at 1, and similarly (2,infinity) is concentrated at 2. As commenters, suggest, there are other ways to interpret your request for an "approximately normal" distribution, such as re-sampling until you hit a value in the required range; or applying a continuous transformation which maps (infinity, infinity) to (1,2), e.g. x -> arctan(x). But you didn't specify what exactly you're after.

Normal Distribution Generator, A tool that will generate a normally distributed dataset based on a specified population mean and standard deviation. Gaussian Random Number Generator This form allows you to generate random numbers from a Gaussian distribution (also known as a normal distribution). The randomness comes from atmospheric noise, which for many purposes is better than the pseudo-random number algorithms typically used in computer programs.

Adding to the other answers, you can use the (pseudo) unform random number generator to make a normal random number generator by using the Polar method

Sample code:

#include <math.h>
#include <stdlib.h>

randn (double mu, double sigma)
  double U1, U2, W, mult;
  static double X1, X2;
  static int call = 0;

  if (call == 1)
      call = !call;
      return (mu + sigma * (double) X2);

      U1 = -1 + ((double) rand () / RAND_MAX) * 2;
      U2 = -1 + ((double) rand () / RAND_MAX) * 2;
      W = pow (U1, 2) + pow (U2, 2);
  while (W >= 1 || W == 0);

  mult = sqrt ((-2 * log (W)) / W);
  X1 = U1 * mult;
  X2 = U2 * mult;

  call = !call;

  return (mu + sigma * (double) X1);

Next, you can use this to get the normally distributed random numbers for your application.

Normal distribution of random numbers (article), var generator = new Random(1);. If we want to produce a random number with a normal (or Gaussian) distribution each time we run through draw() , it's as easy  A “random” normal distribution is just a random set of data that collectively matches the characteristics of a normal distribution. The random normal distribution is one the most common data sets that you’ll want to use to make your data look realistic for real life situations.

You can use std::normal_distribution<> for this.

It generates samples from the full range of the double data type, but you can throw away samples outside the interval you're interested in and you will still be close to a normal distribution with three sigma.

#include <iostream>
#include <random>

using namespace std;

int main()
    auto mean   = 1.5,
         stddev = 1.0 / 6;

    // Create a normal distribution to pull samples from
    // The distribution has mean 1.5 and ~1/6 std dev
    random_device rd;
    mt19937_64 generator(rd());
    normal_distribution<> distribution(mean, stddev);

    cout << "some samples:" << endl;
    for (int i = 0; i < 10; ++i)
        // Generate a sample.  The sample will be in (-infinity, infinity), so 
        // we throw away values that are outside of 3 std devs.
        // The distribution will no longer be normal, but close enough.
        double v;
            v = distribution(generator);
        } while (v < mean - 3 * stddev || v >= mean + 3 * stddev);

        cout << v << endl;
    return 0;

some samples:

Online Gaussian random number generator, Generate random numbers from a Gaussian distribution (also known as a normal distribution) with mean parameter mu and standard deviation parameter sigma  Create a Normally Distributed Set of Random Numbers in Excel Is it possible to create a set of normally distributed values in Excel? Yes, it is, but we will need to look at the cumulative distribution function F(x)=P(X =x) and it's inverse function. This is the probability that a random value from the distribution is less than a given value x.

Random Number Generator - Normal Distribution, This free online software (calculator) generates random numbers for the Normal distribution. The parameters allow you to specify the length of the dataseries to  To transform a standard normal distribution, you multiply your random number by X to get standard deviation X, and you add Y to obtain mean Y, if memory serves me correctly. See the Wikipedia article's section on normalizing standard normal variables (property 1) for a more formal proof.

Random Numbers from Normal Distribution with Specific Mean and , You can apply this concept to get a sample of normally distributed random numbers with mean 500 and variance 25. First, initialize the random number generator  Save the current state of the random number generator and create a 1-by-5 vector of random numbers. Restore the state of the random number generator to s, and then create a new 1-by-5 vector of random numbers. The values are the same as before.

Box–Muller transform, The Box–Muller transform, by George Edward Pelham Box and Mervin Edgar Muller, is a pseudo-random number sampling method for generating pairs of independent, standard, normally distributed (zero expectation, unit variance) random numbers, given Note that because the random number generator rand has not been seeded,  You can use this random number generator to pick a truly random number between any two numbers. For example, to get a random number between 1 and 10, including 10, enter 1 in the first field and 10 in the second, then press "Get Random Number". Our randomizer will pick a number from 1 through 10 at random.

  • This answer would be more useful if you'd modify the distribution to yield an actual probability measure on [1,2].
  • would be useful here. However, collapsing everything into the borders is probably a less desirable approximation than just re-rolling until you hit the right interval to begin with.
  • @BaummitAugen: Oh, I hadn't realized a "clamp" made it into C++17. As for the distribution, that depends on what OP actually wants to achieve.
  • Of course. That's just my interpretation of "approximately normal distribution", which I suspect should not assign positive probability to points. I agree that this is ill-defined in the question, though.
  • Should be std::mt19937 pseudorandom_generator{rd()};