Functions
double	exponential_inverse (double lambda, double u)
	ExponentialDist.inverseF(lambda, u), SSJ's log1p spelling.
double	uniform_inverse (double a, double b, double u)
	UniformDist.inverseF(a, b, u).
double	uniform_int_inverse (double lo, double width, double u)
	UniformIntDist.inverseF(i, j, u), written over the lower bound and the WIDTH w = j - i + 1 so that a lattice shifted off the integers keeps its offset.
double	pareto_inverse (double alpha, double beta, double u)
	ParetoDist.inverseF(alpha, beta, u) = beta (1-u)^(-1/alpha).
double	weibull_inverse (double alpha, double lambda, double delta, double u)
	WeibullDist.inverseF(alpha, lambda, delta, u).
double	bernoulli_inverse (double p, double u)
	BernoulliDist.inverseF(p, u): 1 when u exceeds 1 - p.
double	normal_inverse01 (double u)
	NormalDist.inverseF(0, 1, u) by Wichura's AS 241 (Applied Statistics 37, 1988), the algorithm SSJ's inverseF01 implements.
double	normal_inverse (double mu, double sigma, double u)
	NormalDist.inverseF(mu, sigma, u).
double	lognormal_inverse (double mu, double sigma, double u)
	LognormalDist.inverseF(mu, sigma, u) = exp(mu + sigma Phi^-1(u)).
double	gamma_inverse (double alpha, double lambda, double u)
	GammaDist.inverseF(alpha, lambda, u): the quantile of a Gamma of shape alpha and RATE lambda, so the mean is alpha/lambda, which is SSJ's convention.
double	erlang_inverse (int k, double lambda, double u)
	ErlangGen(k, lambda): the Gamma of integer shape k and rate lambda.
double	poisson_inverse (double lambda, double u)
	PoissonDist.inverseF(lambda, u): the smallest k whose cdf reaches u.
double	binomial_inverse (int n, double p, double u)
	BinomialDist.inverseF(n, p, u), by the same forward inversion.

Function Documentation

◆ bernoulli_inverse()

double line::ldes::ssj::bernoulli_inverse	(	double	p,
		double	u )

inline

BernoulliDist.inverseF(p, u): 1 when u exceeds 1 - p.

Definition at line 117 of file ldes_ssj_variates.h.

References bernoulli_inverse(), and line::InputError::InputError().

Referenced by bernoulli_inverse().

◆ binomial_inverse()

double line::ldes::ssj::binomial_inverse	(	int	n,
		double	p,
		double	u )

inline

BinomialDist.inverseF(n, p, u), by the same forward inversion.

Definition at line 311 of file ldes_ssj_variates.h.

References binomial_inverse(), and line::InputError::InputError().

Referenced by binomial_inverse().

◆ erlang_inverse()

double line::ldes::ssj::erlang_inverse	(	int	k,
		double	lambda,
		double	u )

inline

ErlangGen(k, lambda): the Gamma of integer shape k and rate lambda.

SSJ's ErlangGen inverts the Gamma rather than summing k exponentials, which is why it costs ONE uniform and not k – the measurement above pinned that.

Definition at line 279 of file ldes_ssj_variates.h.

References erlang_inverse(), gamma_inverse(), and line::InputError::InputError().

Referenced by erlang_inverse().

◆ exponential_inverse()

double line::ldes::ssj::exponential_inverse	(	double	lambda,
		double	u )

inline

ExponentialDist.inverseF(lambda, u), SSJ's log1p spelling.

Definition at line 69 of file ldes_ssj_variates.h.

References exponential_inverse(), and line::InputError::InputError().

Referenced by exponential_inverse().

◆ gamma_inverse()

double line::ldes::ssj::gamma_inverse	(	double	alpha,
		double	lambda,
		double	u )

inline

GammaDist.inverseF(alpha, lambda, u): the quantile of a Gamma of shape alpha and RATE lambda, so the mean is alpha/lambda, which is SSJ's convention.

Newton on P(alpha, lambda x) = u from a Wilson-Hilferty start, with a bisection guard: the density vanishes at the origin for alpha > 1 and Newton alone can step negative there. Converges to about 1e-14 relative, which is below the resolution at which a service time can reorder two events.

Definition at line 240 of file ldes_ssj_variates.h.

References gamma_inverse(), line::InputError::InputError(), and normal_inverse01().

Referenced by erlang_inverse(), and gamma_inverse().

◆ lognormal_inverse()

double line::ldes::ssj::lognormal_inverse	(	double	mu,
		double	sigma,
		double	u )

inline

LognormalDist.inverseF(mu, sigma, u) = exp(mu + sigma Phi^-1(u)).

Definition at line 184 of file ldes_ssj_variates.h.

References lognormal_inverse(), and normal_inverse().

Referenced by lognormal_inverse().

◆ normal_inverse()

double line::ldes::ssj::normal_inverse	(	double	mu,
		double	sigma,
		double	u )

inline

NormalDist.inverseF(mu, sigma, u).

Definition at line 178 of file ldes_ssj_variates.h.

References line::InputError::InputError(), normal_inverse(), and normal_inverse01().

Referenced by lognormal_inverse(), and normal_inverse().

◆ normal_inverse01()

double line::ldes::ssj::normal_inverse01 ( double u )

inline

NormalDist.inverseF(0, 1, u) by Wichura's AS 241 (Applied Statistics 37, 1988), the algorithm SSJ's inverseF01 implements.

Accurate to about 1e-16 over the whole range, which is what makes the Lognormal agree with SSJ to the last few bits rather than only to a plotting tolerance.

Definition at line 132 of file ldes_ssj_variates.h.

References normal_inverse01().

Referenced by gamma_inverse(), normal_inverse(), and normal_inverse01().

◆ pareto_inverse()

double line::ldes::ssj::pareto_inverse	(	double	alpha,
		double	beta,
		double	u )

inline

ParetoDist.inverseF(alpha, beta, u) = beta (1-u)^(-1/alpha).

Definition at line 96 of file ldes_ssj_variates.h.

References line::InputError::InputError(), and pareto_inverse().

Referenced by pareto_inverse().

◆ poisson_inverse()

double line::ldes::ssj::poisson_inverse	(	double	lambda,
		double	u )

inline

PoissonDist.inverseF(lambda, u): the smallest k whose cdf reaches u.

Summed forward from k = 0 with the pmf carried recursively. The result is an INTEGER, so it agrees with SSJ exactly whenever the two cdfs put u on the same side of a step, which no test has yet found a counterexample to.

Definition at line 295 of file ldes_ssj_variates.h.

References line::InputError::InputError(), and poisson_inverse().

Referenced by poisson_inverse().

◆ uniform_int_inverse()

double line::ldes::ssj::uniform_int_inverse	(	double	lo,
		double	width,
		double	u )

inline

UniformIntDist.inverseF(i, j, u), written over the lower bound and the WIDTH w = j - i + 1 so that a lattice shifted off the integers keeps its offset.

SSJ computes i + (int)(u*(j - i + 1.0)), clamping the two open ends, and the cast truncates toward zero on a non-negative product, which is the floor.

Definition at line 88 of file ldes_ssj_variates.h.

References line::InputError::InputError(), and uniform_int_inverse().

Referenced by uniform_int_inverse().