sim_dist.h File Reference

Normal and Student t quantiles used by the output-analysis routines. More...

#include <cmath>
#include <limits>
#include <boost/math/special_functions/beta.hpp>
#include <boost/math/special_functions/erf.hpp>
#include "line/util/error.h"

Include dependency graph for sim_dist.h:

Go to the source code of this file.

Namespaces
namespace	line
namespace	line::sim

Functions
double	line::sim::sim_normcdf (double z)
	Standard normal cumulative distribution function.
double	line::sim::sim_norminv (double p)
	Standard normal quantile function.
double	line::sim::sim_tinv (double p, double nu)
	Quantile function of Student's t distribution.

Detailed Description

Normal and Student t quantiles used by the output-analysis routines.

Port of matlab/src/api/sim/sim_normcdf.m, sim_norminv.m and sim_tinv.m, which are grouped here as the JAR groups them in jline.api.sim.SimDist and native Python in line_solver.api.sim.dist. The four codebases reach the same values through four different libraries – MATLAB through erfc/erfinv/betaincinv to avoid a toolbox dependency, the JAR through commons-math3, Python through SciPy and this port through Boost.Math – and agree to within 1e-10.

These are deliberately plain doubles rather than templates on T. A quantile order p and a significance level alpha are doubles at every call site in this family, so the quantile they determine carries double information and no more; see the arithmetic note in sim_types.h.

The t quantile follows the MATLAB identity rather than a distribution object, so the branch structure is comparable line by line with the reference: P(|T| > t) = betainc(nu/(nu+t^2), nu/2, 1/2), inverted for the two-sided tail 2(1-p) and mapped back with t = sqrt(nu (1-z)/z), z = betaincinv(2(1-p), nu/2, 1/2). MATLAB's betaincinv(y, a, b) is Boost's ibeta_inv(a, b, y): both invert the REGULARIZED incomplete beta, and getting the argument order wrong here is a silently plausible wrong number rather than an error.

Definition in file sim_dist.h.