RandLib
With RandLib one can easily work with probability distributions. One of the major advantages of this library (apart from being free and open-source) is that it doesn't require any additional packages. All you need is C++17 compiler support.
What can be done via RandLib? Here are some useful examples:
- Fast sampling. For instance, generate million variates from standard normal distribution:
NormalRand X(0, 1);
std::vector<double> data(1e6);
X.Sample(data);
- Calculate moments and other properties:
LogNormalRand X(1, 1);
std::cout << " Mean = " << X.Mean()
<< " and Variance = " << X.Variance()
<< "\n Median = " << X.Median()
<< " and Mode = " << X.Mode()
<< "\n Skewness = " << X.Skewness()
<< " and Excess kurtosis = " << X.ExcessKurtosis();
Mean = 4.48169 and Variance = 34.5126
Median = 2.71828 and Mode = 1
Skewness = 6.18488 and Excess Kurtosis = 110.936
- Fitting parameters using different estimators:
using std::cout;
NormalRand X(0, 1);
std::vector<double> data(10);
X.Sample(data);
cout << "True distribution: " << X.Name() << "\n";
cout << "Sample: ";
for (double var : data)
cout << var << " ";
cout << "\n";
/// Bayesian estimation
NormalInverseGammaRand prior(0, 1, 1, 1);
NormalInverseGammaRand posterior = X.FitBayes(data, prior);
cout << "Bayesian estimator: " << X.Name() << "\n";
cout << "(Posterior distribution: " << posterior.Name() << ")\n";
/// Uniformly minimum variance unbiased estimator
X.Fit(data, true);
cout << "UMVU estimator: " << X.Name() << "\n";
/// Maximum-likelihood estimator
X.Fit(data);
cout << "Maximum-likelihood estimator: " << X.Name() << "\n";
True distribution: Normal(0, 1)
Sample: -0.328154 0.709122 -0.607214 1.11472 -1.23726 -0.123584 0.59374 -1.20573 -0.397376 -1.63173
Bayesian estimator: Normal(-0.283042, 0.951348)
(Posterior distribution: Normal-Inverse-Gamma(-0.283042, 11, 6, 4.75674))
UMVU estimator: Normal(-0.311347, 0.82504)
Maximum-likelihood estimator: Normal(-0.311347, 0.742536)
For documentation look up here