I don't know if this is directly pertinent to you, depending on what platforms you want to support. If it's not feel free to close the issue.

There are a multitude of places throughout the code base that use the identifier constexpr, but make calls to std::pow, std::log, and std::sqrt in the definitions. These are not actually defined as constexpr in the c++ standard (see this stackoverflow post) and as such any standard compiler other than GCC will throw errors when trying to compile the library.

I have made a workaround for this on my personal fork of this repository using a few header only files from the kthohr/gcem library. I don't know if you want to bring in external libraries but it is at least worth looking at if you need a launch point. Likewise, you are welcome to review my fork for reference. If you want I will be happy to open a pull request from that fork here, but there are significant modifications to the structuring and include paths on mine (It's currently a work in progress).

e.g. is it possible to calculate the pdf of a normal distribution (and store it in a vector)?

On line 533 of StableRand.cpp the variable theta0 is uninitialized when used 2 lines later.

Most of the properties of log-stable distribution are easy to derive using the relationship with stable distribution. However, the problem arises with characteristic function, which can't be expressed analytically and is hard to compute numerically due to singularity of probability density function at point 0 in some cases (e.g. Log-Cauchy distribution). All ideas are welcome.

Use Fit() for MLE and Fit(unbiased = true) for UMVU. Remove method of moments

cloned this repository.
But in Qt creator has problem : no viable constructor or deduction guide for deduction of template arguments of 'NormalRand';
Wrote code according your manual
NormalRand X(0, 1);
std::vector data(1e6);
X.Sample(data);

Implement different numerical integration algorithms (e.g. adaptive Gauss-Kronrod quadrature) and apply in appropriate cases

• Numerical integration as in this paper: A Note on Computing Extreme Tail Probabilities of the Noncentral T Distribution with Large Noncentrality Parameter
• Series expansion as on Wikipedia page

The problems are with

• alpha close to 1 with non-zero beta
• beta close to 0, when alpha = 1
• asymptotic series expansion for alpha = 1 and non-zero beta
• cdf representation for short tails (beta = 1)

There is no way these values could be properly represented as the long double type you defined them as. See this article from GeeksforGeeks for a simple reference on why this occurs and how this could be affecting your intended values. And this StackOverflow post is pertinent because of the type declaration.

Find n and p (very small), such that BinomialRand variate generator can be replaced with PoissonRand generator

• logarithm of modified Bessel function of the first and second kind

• lower and upper incomplete gamma functions (and their logarithms)

• Marcum-Q and Marcum-P functions

• erfinv and erfcinv

• incomplete beta function

• maximum likelihood fit: f(a-eps) < f(a) < f(a+eps)

• mode value: f(x-eps) < f(x) < f(x+eps)

• pdf and logpdf coherence: f(x) = exp(logf(x))

We integrate numerically on semi-finite interval in order to get CF of LogNormalRand. However, there exist at least two more ways to do it:

• we can use divergent Taylor series expansion
• or the Laplace transform, described in this 📝 , which requires implementation of Lambert-W function for pure imaginary argument

• Use structured bindings, e.g.
  auto [a, b, c] = array
  instead of
  std::tie(a, b, c) = array
  Search by DoublePair or std::tuple. This could also be useful for loops through tuple arrays (if one uses std::map in pdf for example)
• Init statements for if / switch (look for temp variables)