StatsLib

StatsLib is a templated C++ library of statistical distribution functions.

Features:

A header-only library of probability density functions, cumulative distribution functions, quantile functions, and random sampling methods.
Functions are written in C++11 constexpr format.
- Built on the GCE-Math library, StatsLib can operate as a compile-time or run-time computation engine.
A simple, R-like syntax.
Optional vector-matrix functionality with wrappers to support several popular linear algebra libraries, including:
- Armadillo
- Blaze
- Eigen
Matrix-based operations are parallelizable with OpenMP.
Released under a permissive, non-GPL license.

Distributions

Functions to compute the cdf, pdf, and quantile, as well as random sampling, are available for the following distributions:

Bernoulli
Beta
Binomial
Cauchy
Chi-squared
Exponential
F
Gamma
Inverse-Gamma
Laplace
Logistic
Log-Normal
Normal (Gaussian)
Poisson
Student's t
Uniform
Weibull

In addition, pdf and random sampling functions are available for several multivariate distributions:

inverse-Wishart
Multivariate Normal
Wishart

Installation

StatsLib is a header-only library. Simply copy the contents of the include folder and add the header files to your project using

#include "stats.hpp"

Compile-time Options

For inline-only functionality (i.e., no constexpr specifiers):

#define STATS_GO_INLINE

OpenMP functionality is enabled by default if the _OPENMP macro is detected (e.g., by invoking -fopenmp with a GCC or Clang compiler). To explicitly enable OpenMP features use:

#define STATS_USE_OPENMP

To disable OpenMP functionality:

#define STATS_DONT_USE_OPENMP

To use StatsLib with the Armadillo, Blaze or Eigen libraries:

#define STATS_USE_ARMA
#define STATS_USE_BLAZE
#define STATS_USE_EIGEN

Syntax and Examples

Functions are called using an R-like syntax. Some general rules:

density functions: stats::d*. For example, the Normal (Gaussian) density is called using

stats::dnorm(<value>,<mean parameter>,<standard deviation>);

cumulative distribution functions: stats::p*. For example, the Gamma CDF is called using

stats::pgamma(<value>,<shape parameter>,<scale parameter>);

quantile functions: stats::q*. For example, the Beta quantile is called using

stats::qbeta(<value>,<a parameter>,<b parameter>);

random sampling: stats::r*. For example, to generate a single draw from the Logistic distribution:

stats::rlogis(<location parameter>,<scale parameter>,<seed value or random number engine>);

All of these functions have matrix-based equivalents using Armadillo, Blaze, and Eigen dense matrices.

The pdf, cdf, and quantile functions can take matrix-valued arguments. For example,

// Using Armadillo:
arma::mat norm_pdf_vals = stats::dnorm(arma::ones(10,20),1.0,2.0);

The randomization functions (r*) can output random matrices of arbitrary size. For example,

// Armadillo:
arma::mat gamma_rvs = stats::rgamma<arma::mat>(100,50,3.0,2.0);
// Blaze:
blaze::DynamicMatrix<double> gamma_rvs = stats::rgamma<blaze::DynamicMatrix<double>>(100,50,3.0,2.0);
// Eigen:
Eigen::MatrixXd gamma_rvs = stats::rgamma<Eigen::MatrixXd>(100,50,3.0,2.0);

will generate a 100-by-50 matrix of iid draws from a Gamma(3,2) distribution.

All matrix-based operations are parallelizable with OpenMP. For GCC and Clang compilers, simply include the -fopenmp option during compilation.

Random number seeding is available in two forms: seed values or random number engines (preferred).

Seed values are passed as unsigned integers. For example, to generate a draw from a normal distribution N(1,2) with seed value 1776:

stats::rnorm(1,2,1776);

Random engines in StatsLib use the 64-bit Mersenne-Twister generator (std::mt19937_64) and are passed by reference. Example:

std::mt19937_64 engine(1776);
stats::rnorm(1,2,engine);

More examples with code:

// evaluate the normal PDF at x = 1, mu = 0, sigma = 1
double dval_1 = stats::dnorm(1.0,0.0,1.0);
 
// evaluate the normal PDF at x = 1, mu = 0, sigma = 1, and return the log value
double dval_2 = stats::dnorm(1.0,0.0,1.0,true);
 
// evaluate the normal CDF at x = 1, mu = 0, sigma = 1
double pval = stats::pnorm(1.0,0.0,1.0);
 
// evaluate the Laplacian quantile at p = 0.1, mu = 0, sigma = 1
double qval = stats::qlaplace(0.1,0.0,1.0);

// draw from a t-distribution dof = 30
double rval = stats::rt(30);

// matrix output
arma::mat beta_rvs = stats::rbeta<arma::mat>(100,100,3.0,2.0);
// matrix input
arma::mat beta_cdf_vals = stats::pbeta(beta_rvs,3.0,2.0);

Compile-time Computation

In addition to being a standard run-time library, StatsLib can operate as a compile-time computation engine. Compile-time features are enabled using the constexpr specifier:

#include "stats.hpp"

int main()
{
    
    constexpr double dens_1  = stats::dlaplace(1.0,1.0,2.0); // answer = 0.25
    constexpr double prob_1  = stats::plaplace(1.0,1.0,2.0); // answer = 0.5
    constexpr double quant_1 = stats::qlaplace(0.1,1.0,2.0); // answer = -2.218875...

    return 0;
}

Assembly code generated by Clang:

LCPI0_0:
	.quad	-4611193153885729483    ## double -2.2188758248682015
LCPI0_1:
	.quad	4602678819172646912     ## double 0.5
LCPI0_2:
	.quad	4598175219545276417     ## double 0.25000000000000006
	.section	__TEXT,__text,regular,pure_instructions
	.globl	_main
	.p2align	4, 0x90
_main:                                  ## @main
	push	rbp
	mov	rbp, rsp
	xor	eax, eax
	movsd	xmm0, qword ptr [rip + LCPI0_0] ## xmm0 = mem[0],zero
	movsd	xmm1, qword ptr [rip + LCPI0_1] ## xmm1 = mem[0],zero
	movsd	xmm2, qword ptr [rip + LCPI0_2] ## xmm2 = mem[0],zero
	mov	dword ptr [rbp - 4], 0
	movsd	qword ptr [rbp - 16], xmm2
	movsd	qword ptr [rbp - 24], xmm1
	movsd	qword ptr [rbp - 32], xmm0
	pop	rbp
	ret

Author

Keith O'Hara

License

Apache Version 2

a-ma72 / stats