Implements various probability distributions. Almost all code is courtesy of Riastradh. More...

#include "orconfig.h"
#include "lib/math/prob_distr.h"
#include "lib/crypt_ops/crypto_rand.h"
#include "lib/cc/ctassert.h"
#include "lib/log/util_bug.h"
#include <float.h>
#include <math.h>
#include <stddef.h>

Macros
#define	PROB_DISTR_PRIVATE

#define	DECLARE_PROB_DISTR_DOWNCAST_FN(name)

Functions
static unsigned	bitcount32 (uint32_t x)

static unsigned	clz32 (uint32_t x)

STATIC double	logistic (double x)

STATIC double	logit (double p)

STATIC double	logithalf (double p0)

	CTASSERT (FLT_RADIX==2)

	CTASSERT (-DBL_MIN_EXP<=1021)

	CTASSERT (DBL_MANT_DIG<=53)

STATIC double	random_uniform_01 (void)

STATIC double	cdf_logistic (double x, double mu, double sigma)

STATIC double	sf_logistic (double x, double mu, double sigma)

STATIC double	icdf_logistic (double p, double mu, double sigma)

STATIC double	isf_logistic (double p, double mu, double sigma)

STATIC double	cdf_log_logistic (double x, double alpha, double beta)

STATIC double	sf_log_logistic (double x, double alpha, double beta)

STATIC double	icdf_log_logistic (double p, double alpha, double beta)

STATIC double	isf_log_logistic (double p, double alpha, double beta)

STATIC double	cdf_weibull (double x, double lambda, double k)

STATIC double	sf_weibull (double x, double lambda, double k)

STATIC double	icdf_weibull (double p, double lambda, double k)

STATIC double	isf_weibull (double p, double lambda, double k)

STATIC double	cdf_genpareto (double x, double mu, double sigma, double xi)

STATIC double	sf_genpareto (double x, double mu, double sigma, double xi)

STATIC double	icdf_genpareto (double p, double mu, double sigma, double xi)

STATIC double	isf_genpareto (double p, double mu, double sigma, double xi)

STATIC double	sample_uniform_interval (double p0, double a, double b)

STATIC double	sample_logistic (uint32_t s, double t, double p0)

static double	sample_logistic_locscale (uint32_t s, double t, double p0, double mu, double sigma)

STATIC double	sample_log_logistic (uint32_t s, double p0)

static double	sample_log_logistic_scaleshape (uint32_t s, double p0, double alpha, double beta)

static double	sample_exponential (uint32_t s, double p0)

STATIC double	sample_weibull (uint32_t s, double p0, double lambda, double k)

STATIC double	sample_genpareto (uint32_t s, double p0, double xi)

static double	sample_genpareto_locscale (uint32_t s, double p0, double mu, double sigma, double xi)

static double	sample_geometric (uint32_t s, double p0, double p)

const char *	dist_name (const struct dist_t *dist)

double	dist_sample (const struct dist_t *dist)

double	dist_cdf (const struct dist_t *dist, double x)

double	dist_sf (const struct dist_t *dist, double x)

double	dist_icdf (const struct dist_t *dist, double p)

double	dist_isf (const struct dist_t *dist, double p)

static double	uniform_sample (const struct dist_t *dist)

static double	uniform_cdf (const struct dist_t *dist, double x)

static double	uniform_sf (const struct dist_t *dist, double x)

static double	uniform_icdf (const struct dist_t *dist, double p)

static double	uniform_isf (const struct dist_t *dist, double p)

static double	logistic_sample (const struct dist_t *dist)

static double	logistic_cdf (const struct dist_t *dist, double x)

static double	logistic_sf (const struct dist_t *dist, double x)

static double	logistic_icdf (const struct dist_t *dist, double p)

static double	logistic_isf (const struct dist_t *dist, double p)

static double	log_logistic_sample (const struct dist_t *dist)

static double	log_logistic_cdf (const struct dist_t *dist, double x)

static double	log_logistic_sf (const struct dist_t *dist, double x)

static double	log_logistic_icdf (const struct dist_t *dist, double p)

static double	log_logistic_isf (const struct dist_t *dist, double p)

static double	weibull_sample (const struct dist_t *dist)

static double	weibull_cdf (const struct dist_t *dist, double x)

static double	weibull_sf (const struct dist_t *dist, double x)

static double	weibull_icdf (const struct dist_t *dist, double p)

static double	weibull_isf (const struct dist_t *dist, double p)

static double	genpareto_sample (const struct dist_t *dist)

static double	genpareto_cdf (const struct dist_t *dist, double x)

static double	genpareto_sf (const struct dist_t *dist, double x)

static double	genpareto_icdf (const struct dist_t *dist, double p)

static double	genpareto_isf (const struct dist_t *dist, double p)

static double	geometric_sample (const struct dist_t *dist)

static double	geometric_cdf (const struct dist_t *dist, double x)

static double	geometric_sf (const struct dist_t *dist, double x)

static double	geometric_icdf (const struct dist_t *dist, double p)

static double	geometric_isf (const struct dist_t *dist, double p)

Variables
const struct dist_ops_t	uniform_ops

const struct dist_ops_t	logistic_ops

const struct dist_ops_t	log_logistic_ops

const struct dist_ops_t	weibull_ops

const struct dist_ops_t	genpareto_ops

const struct dist_ops_t	geometric_ops

Detailed Description

Implements various probability distributions. Almost all code is courtesy of Riastradh.

Here are some details that might help you understand this file:

Throughout this file, ‘eps’ means the largest relative error of a correctly rounded floating-point operation, which in binary64 floating-point arithmetic is 2^-53. Here the relative error of a true value x from a computed value y is |x - y|/|x|. This definition of epsilon is conventional for numerical analysts when writing error analyses. (If your libm doesn't provide correctly rounded exp and log, their relative error is usually below 2*2^-53 and probably closer to 1.1*2^-53 instead.)

The C constant DBL_EPSILON is actually twice this, and should perhaps rather be named ulp(1) – that is, it is the distance from 1 to the next greater floating-point number, which is usually of more interest to programmers and hardware engineers.

Since this file is concerned mainly with error bounds rather than with low-level bit-hacking of floating-point numbers, we adopt the numerical analysts' definition in the comments, though we do use DBL_EPSILON in a handful of places where it is convenient to use some function of eps = DBL_EPSILON/2 in a case analysis.
In various functions (e.g. sample_log_logistic()) we jump through hoops so that we can use reals closer to 0 than closer to 1, since we achieve much greater accuracy for floating point numbers near 0. In particular, we can represent differences as small as 10^-300 for numbers near 0, but of no less than 10^-16 for numbers near 1.

Definition in file prob_distr.c.

Macro Definition Documentation

◆ DECLARE_PROB_DISTR_DOWNCAST_FN

#define DECLARE_PROB_DISTR_DOWNCAST_FN ( name )

Value:

  static inline                           \
  const struct name##_t *                             \
  dist_to_const_##name(const struct dist_t *obj) {    \
    tor_assert(obj->ops == &name##_ops);            \
    return SUBTYPE_P(obj, struct name ## _t, base);   \
  }

Declare a function that downcasts from a generic dist struct to the actual subtype probablity distribution it represents.

Definition at line 58 of file prob_distr.c.

Function Documentation

◆ bitcount32()

static unsigned bitcount32 ( uint32_t x )

static

Count number of one bits in 32-bit word.

Definition at line 77 of file prob_distr.c.

Referenced by clz32().

◆ cdf_genpareto()

STATIC double cdf_genpareto	(	double	x,
		double	mu,
		double	sigma,
		double	xi
	)

Compute the CDF of the GeneralizedPareto(mu, sigma, xi) distribution. Well-conditioned everywhere. For standard distribution (mu=0, sigma=1), condition number

 (x/(1 + x xi)) / ((1 + x xi)^{1/xi} - 1)

is bounded by 1, attained only at x = 0.

Definition at line 792 of file prob_distr.c.

◆ cdf_log_logistic()

STATIC double cdf_log_logistic	(	double	x,
		double	alpha,
		double	beta
	)

Compute the CDF of the LogLogistic(alpha, beta) distribution. Well-conditioned for all x and alpha, and the condition number

 -beta/[1 + (x/alpha)^{-beta}]

grows linearly with beta.

Loosely, the relative error of this implementation is bounded by

 4 eps + 2 eps^2 + O(beta eps),

so don't bother trying this for beta anywhere near as large as 1/eps, around which point it levels off at 1.

Definition at line 598 of file prob_distr.c.

◆ cdf_logistic()

STATIC double cdf_logistic	(	double	x,
		double	mu,
		double	sigma
	)

Compute the CDF of the Logistic(mu, sigma) distribution: the logistic function. Well-conditioned for negative inputs and small positive inputs; ill-conditioned for large positive inputs.

Definition at line 511 of file prob_distr.c.

◆ cdf_weibull()

STATIC double cdf_weibull	(	double	x,
		double	lambda,
		double	k
	)

Compute the CDF of the Weibull(lambda, k) distribution. Well-conditioned for small x and k, and for large lambda – condition number

 -k (x/lambda)^k exp(-(x/lambda)^k)/[exp(-(x/lambda)^k) - 1]

grows linearly with k, x^k, and lambda^{-k}.

Definition at line 711 of file prob_distr.c.

◆ clz32()

static unsigned clz32 ( uint32_t x )

static

Count leading zeros in 32-bit word.

Definition at line 97 of file prob_distr.c.

Referenced by random_uniform_01().

◆ dist_cdf()

double dist_cdf	(	const struct dist_t *	dist,
		double	x
	)

Compute the CDF of dist at x.

Definition at line 1345 of file prob_distr.c.

◆ dist_icdf()

double dist_icdf	(	const struct dist_t *	dist,
		double	p
	)

Compute the iCDF (Inverse CDF) of dist at x.

Definition at line 1359 of file prob_distr.c.

◆ dist_isf()

double dist_isf	(	const struct dist_t *	dist,
		double	p
	)

Compute the iSF (Inverse Survival function) of dist at x.

Definition at line 1366 of file prob_distr.c.

◆ dist_name()

const char* dist_name ( const struct dist_t * dist )

Public API for probability distributions:

These are wrapper functions on top of the various probability distribution operations using the generic dist structure.

These are the functions that should be used by consumers of this API. Returns the name of the distribution in dist.

Definition at line 1331 of file prob_distr.c.

◆ dist_sf()

double dist_sf	(	const struct dist_t *	dist,
		double	x
	)

Compute the SF (Survival function) of dist at x.

Definition at line 1352 of file prob_distr.c.

◆ genpareto_sample()

static double genpareto_sample ( const struct dist_t * dist )

static

Functions for generalized Pareto distributions

Definition at line 1589 of file prob_distr.c.

◆ geometric_sample()

static double geometric_sample ( const struct dist_t * dist )

static

Functions for geometric distribution on number of trials before success

Definition at line 1638 of file prob_distr.c.

◆ icdf_genpareto()

STATIC double icdf_genpareto	(	double	p,
		double	mu,
		double	sigma,
		double	xi
	)

Compute the inverse of the CDF of the GeneralizedPareto(mu, sigma, xi) distribution. Ill-conditioned for p near 1; condition number is

 xi (p/(1 - p))/(1 - (1 - p)^xi)

Definition at line 853 of file prob_distr.c.

◆ icdf_log_logistic()

STATIC double icdf_log_logistic	(	double	p,
		double	alpha,
		double	beta
	)

Compute the inverse of the CDF of the LogLogistic(alpha, beta) distribution. Ill-conditioned for p near 1 and beta near 0 with condition number 1/[beta (1 - p)].

Definition at line 675 of file prob_distr.c.

◆ icdf_logistic()

STATIC double icdf_logistic	(	double	p,
		double	mu,
		double	sigma
	)

Compute the inverse of the CDF of the Logistic(mu, sigma) distribution: the logit function. Well-conditioned near 0; ill-conditioned near 1/2 and 1.

Definition at line 534 of file prob_distr.c.

◆ icdf_weibull()

STATIC double icdf_weibull	(	double	p,
		double	lambda,
		double	k
	)

Compute the inverse of the CDF of the Weibull(lambda, k) distribution. Ill-conditioned for p near 1, and for k near 0; condition number is

 (p/(1 - p))/(k log(1 - p)).

Definition at line 739 of file prob_distr.c.

◆ isf_genpareto()

STATIC double isf_genpareto	(	double	p,
		double	mu,
		double	sigma,
		double	xi
	)

Compute the inverse of the SF of the GeneralizedPareto(mu, sigma, xi) distribution. Ill-conditioned for p near 1; condition number is

 -xi/(1 - p^{-xi})

Definition at line 899 of file prob_distr.c.

◆ isf_log_logistic()

STATIC double isf_log_logistic	(	double	p,
		double	alpha,
		double	beta
	)

Compute the inverse of the SF of the LogLogistic(alpha, beta) distribution. Ill-conditioned for p near 1 and for large beta, with condition number -1/[beta (1 - p)].

Definition at line 686 of file prob_distr.c.

◆ isf_logistic()

STATIC double isf_logistic	(	double	p,
		double	mu,
		double	sigma
	)

Compute the inverse of the SF of the Logistic(mu, sigma) distribution: the -logit function. Well-conditioned near 0; ill-conditioned near 1/2 and 1.

Definition at line 545 of file prob_distr.c.

◆ isf_weibull()

STATIC double isf_weibull	(	double	p,
		double	lambda,
		double	k
	)

Compute the inverse of the SF of the Weibull(lambda, k) distribution. Ill-conditioned for p near 0, and for k near 0; condition number is

 1/(k log(p)).

Definition at line 752 of file prob_distr.c.

◆ log_logistic_sample()

static double log_logistic_sample ( const struct dist_t * dist )

static

Functions for log-logistic distribution:

Definition at line 1491 of file prob_distr.c.

◆ logistic()

STATIC double logistic ( double x )

Compute the logistic function: f(x) = 1/(1 + e^{-x}) = e^x/(1 + e^x). Maps a log-odds-space probability in [-infinity, +infinity] into a direct-space probability in [0,1]. Inverse of logit.

Ill-conditioned for large x; the identity logistic(-x) = 1 - logistic(x) and the function logistichalf(x) = logistic(x) - 1/2 may help to rearrange a computation.

This implementation gives relative error bounded by 7 eps.

Definition at line 193 of file prob_distr.c.

Referenced by cdf_logistic(), and sf_logistic().

◆ logistic_sample()

static double logistic_sample ( const struct dist_t * dist )

static

Private functions for each probability distribution. Functions for logistic distribution:

Definition at line 1441 of file prob_distr.c.

◆ logit()

STATIC double logit ( double p )

Compute the logit function: log p/(1 - p). Defined on [0,1]. Maps a direct-space probability in [0,1] to a log-odds-space probability in [-infinity, +infinity]. Inverse of logistic.

Ill-conditioned near 1/2 and 1; the identity logit(1 - p) = -logit(p) and the function logithalf(p0) = logit(1/2 + p0) may help to rearrange a computation for p in [1/(1 + e), 1 - 1/(1 + e)].

This implementation gives relative error bounded by 10 eps.

Definition at line 280 of file prob_distr.c.

Referenced by icdf_logistic(), isf_logistic(), and sample_logistic().

◆ logithalf()

STATIC double logithalf ( double p0 )

Compute the logit function, translated in input by 1/2: logithalf(p) = logit(1/2 + p). Defined on [-1/2, 1/2]. Inverse of logistichalf.

Ill-conditioned near +/-1/2. If |p0| > 1/2 - 1/(1 + e), it may be better to compute 1/2 + p0 or -1/2 - p0 and to use logit instead. This implementation gives relative error bounded by 34 eps.

Definition at line 360 of file prob_distr.c.

Referenced by sample_logistic().

◆ random_uniform_01()

STATIC double random_uniform_01 ( void )

Draw a floating-point number in [0, 1] with uniform distribution.

Note that the probability of returning 0 is less than 2^-1074, so callers need not check for it. However, callers that cannot handle rounding to 1 must deal with that, because it occurs with probability 2^-54, which is small but nonnegligible.

Definition at line 453 of file prob_distr.c.

Referenced by genpareto_sample(), geometric_sample(), log_logistic_sample(), logistic_sample(), uniform_sample(), and weibull_sample().

◆ sample_exponential()

static double sample_exponential	(	uint32_t	s,
		double	p0
	)

static

Deterministically sample from the standard exponential distribution, indexed by a uniform random 32-bit integer s and a uniform random floating-point number p0 in (0, 1].

Definition at line 1196 of file prob_distr.c.

Referenced by sample_genpareto(), and sample_geometric().

◆ sample_genpareto()

STATIC double sample_genpareto	(	uint32_t	s,
		double	p0,
		double	xi
	)

Deterministically sample from the generalized Pareto distribution with shape xi, indexed by a uniform random 32-bit integer s and a uniform random floating-point number p0 in (0, 1].

Definition at line 1231 of file prob_distr.c.

Referenced by sample_genpareto_locscale().

◆ sample_genpareto_locscale()

static double sample_genpareto_locscale	(	uint32_t	s,
		double	p0,
		double	mu,
		double	sigma,
		double	xi
	)

static

Deterministically sample from a generalized Pareto distribution with shape xi, scaled by sigma and translated by mu.

Definition at line 1277 of file prob_distr.c.

Referenced by genpareto_sample().

◆ sample_geometric()

static double sample_geometric	(	uint32_t	s,
		double	p0,
		double	p
	)

static

Deterministically sample from the geometric distribution with per-trial success probability p.

Definition at line 1307 of file prob_distr.c.

Referenced by geometric_sample().

◆ sample_log_logistic()

STATIC double sample_log_logistic	(	uint32_t	s,
		double	p0
	)

Deterministically sample from the standard log-logistic distribution, indexed by a uniform random 32-bit integer s and a uniform random floating-point number p0 in (0, 1].

Definition at line 1160 of file prob_distr.c.

Referenced by sample_log_logistic_scaleshape().

◆ sample_log_logistic_scaleshape()

static double sample_log_logistic_scaleshape	(	uint32_t	s,
		double	p0,
		double	alpha,
		double	beta
	)

static

Deterministically sample from the log-logistic distribution with scale alpha and shape beta.

Definition at line 1182 of file prob_distr.c.

Referenced by log_logistic_sample().

◆ sample_logistic()

STATIC double sample_logistic	(	uint32_t	s,
		double	t,
		double	p0
	)

Deterministically sample from the standard logistic distribution, indexed by a uniform random 32-bit integer s and uniform random floating-point numbers t and p0 in (0, 1].

Definition at line 1094 of file prob_distr.c.

Referenced by sample_logistic_locscale().

◆ sample_logistic_locscale()

static double sample_logistic_locscale	(	uint32_t	s,
		double	t,
		double	p0,
		double	mu,
		double	sigma
	)

static

Deterministically sample from the logistic distribution scaled by sigma and translated by mu.

Definition at line 1147 of file prob_distr.c.

Referenced by logistic_sample().

◆ sample_uniform_interval()

STATIC double sample_uniform_interval	(	double	p0,
		double	a,
		double	b
	)

Deterministic samplers, parametrized by uniform integer and (0,1] samples. No guarantees are made about which mapping from the integer and (0,1] samples these use; all that is guaranteed is the distribution of the outputs conditioned on a uniform distribution on the inputs. The automatic tests in test_prob_distr.c double-check the particular mappings we use.

Beware: Unlike random_uniform_01(), these are not guaranteed to be supported on all possible outputs. See Ilya Mironov, `On the Significance of the Least Significant Bits for Differential Privacy', for an example of what can go wrong if you try to use these to conceal information from an adversary but you expose the specific full-precision floating-point values.

Note: None of these samplers use rejection sampling; they are all essentially inverse-CDF transforms with tweaks. If you were to add, say, a Gamma sampler with the Marsaglia-Tsang method, you would have to parametrize it by a potentially infinite stream of uniform (and perhaps normal) samples rather than a fixed number, which doesn't make for quite as nice automatic testing as for these. Deterministically sample from the interval [a, b], indexed by a uniform random floating-point number p0 in (0, 1].

Note that even if p0 is nonzero, the result may be equal to a, if ulp(a)/2 is nonnegligible, e.g. if a = 1. For maximum resolution, arrange |a| <= |b|.

Definition at line 941 of file prob_distr.c.

Referenced by uniform_sample().

◆ sample_weibull()

STATIC double sample_weibull	(	uint32_t	s,
		double	p0,
		double	lambda,
		double	k
	)

Deterministically sample from a Weibull distribution with scale lambda and shape k – just an exponential with a shape parameter in addition to a scale parameter. (Yes, lambda really is the scale, not the rate.)

Definition at line 1219 of file prob_distr.c.

Referenced by weibull_sample().

◆ sf_genpareto()

STATIC double sf_genpareto	(	double	x,
		double	mu,
		double	sigma,
		double	xi
	)

Compute the SF of the GeneralizedPareto(mu, sigma, xi) distribution. For standard distribution (mu=0, sigma=1), ill-conditioned for xi near 0; condition number

 -x (1 + x xi)^{(-1 - xi)/xi}/(1 + x xi)^{-1/xi}
 = -x (1 + x xi)^{-1/xi - 1}/(1 + x xi)^{-1/xi}
 = -(x/(1 + x xi)) (1 + x xi)^{-1/xi}/(1 + x xi)^{-1/xi}
 = -x/(1 + x xi)

is bounded by 1/xi.

Definition at line 836 of file prob_distr.c.

◆ sf_log_logistic()

STATIC double sf_log_logistic	(	double	x,
		double	alpha,
		double	beta
	)

Compute the SF of the LogLogistic(alpha, beta) distribution. Well-conditioned for all x and alpha, and the condition number

 beta/[1 + (x/alpha)^beta]

grows linearly with beta.

Loosely, the relative error of this implementation is bounded by

 4 eps + 2 eps^2 + O(beta eps)

so don't bother trying this for beta anywhere near as large as 1/eps, beyond which point it grows unbounded.

Definition at line 659 of file prob_distr.c.

◆ sf_logistic()

STATIC double sf_logistic	(	double	x,
		double	mu,
		double	sigma
	)

Compute the SF of the Logistic(mu, sigma) distribution: the logistic function reflected over the y axis. Well-conditioned for positive inputs and small negative inputs; ill-conditioned for large negative inputs.

Definition at line 523 of file prob_distr.c.

◆ sf_weibull()

STATIC double sf_weibull	(	double	x,
		double	lambda,
		double	k
	)

Compute the SF of the Weibull(lambda, k) distribution. Well-conditioned for small x and k, and for large lambda – condition number

 -k (x/lambda)^k

grows linearly with k, x^k, and lambda^{-k}.

Definition at line 726 of file prob_distr.c.

◆ uniform_sample()

static double uniform_sample ( const struct dist_t * dist )

static

Functions for uniform distribution

Definition at line 1374 of file prob_distr.c.

◆ weibull_sample()

static double weibull_sample ( const struct dist_t * dist )

static

Functions for Weibull distribution

Definition at line 1540 of file prob_distr.c.

Variable Documentation

◆ genpareto_ops

const struct dist_ops_t genpareto_ops

Initial value:

= {
  .name = "generalized Pareto",
  .sample = genpareto_sample,
  .cdf = genpareto_cdf,
  .sf = genpareto_sf,
  .icdf = genpareto_icdf,
  .isf = genpareto_isf,
}

Definition at line 1620 of file prob_distr.c.

◆ geometric_ops

const struct dist_ops_t geometric_ops

Initial value:

= {
  .name = "geometric (1-based)",
  .sample = geometric_sample,
  .cdf = geometric_cdf,
  .sf = geometric_sf,
  .icdf = geometric_icdf,
  .isf = geometric_isf,
}

Definition at line 1678 of file prob_distr.c.

◆ log_logistic_ops

const struct dist_ops_t log_logistic_ops

Initial value:

= {
  .name = "log logistic",
  .sample = log_logistic_sample,
  .cdf = log_logistic_cdf,
  .sf = log_logistic_sf,
  .icdf = log_logistic_icdf,
  .isf = log_logistic_isf,
}

Definition at line 1522 of file prob_distr.c.

◆ logistic_ops

const struct dist_ops_t logistic_ops

Initial value:

= {
  .name = "logistic",
  .sample = logistic_sample,
  .cdf = logistic_cdf,
  .sf = logistic_sf,
  .icdf = logistic_icdf,
  .isf = logistic_isf,
}

Definition at line 1473 of file prob_distr.c.

◆ uniform_ops

const struct dist_ops_t uniform_ops

Initial value:

= {
  .name = "uniform",
  .sample = uniform_sample,
  .cdf = uniform_cdf,
  .sf = uniform_sf,
  .icdf = uniform_icdf,
  .isf = uniform_isf,
}

Definition at line 1417 of file prob_distr.c.

◆ weibull_ops

const struct dist_ops_t weibull_ops

Initial value:

= {
  .name = "Weibull",
  .sample = weibull_sample,
  .cdf = weibull_cdf,
  .sf = weibull_sf,
  .icdf = weibull_icdf,
  .isf = weibull_isf,
}

Definition at line 1571 of file prob_distr.c.

Macros

Functions

Variables

Detailed Description

Macro Definition Documentation

◆ DECLARE_PROB_DISTR_DOWNCAST_FN

Function Documentation

◆ bitcount32()

◆ cdf_genpareto()

◆ cdf_log_logistic()

◆ cdf_logistic()

◆ cdf_weibull()

◆ clz32()

◆ dist_cdf()

◆ dist_icdf()

◆ dist_isf()

◆ dist_name()

◆ dist_sf()

◆ genpareto_sample()

◆ geometric_sample()

◆ icdf_genpareto()

◆ icdf_log_logistic()

◆ icdf_logistic()

◆ icdf_weibull()

◆ isf_genpareto()

◆ isf_log_logistic()

◆ isf_logistic()

◆ isf_weibull()

◆ log_logistic_sample()

◆ logistic()

◆ logistic_sample()

◆ logit()

◆ logithalf()

◆ random_uniform_01()

◆ sample_exponential()

◆ sample_genpareto()

◆ sample_genpareto_locscale()

◆ sample_geometric()

◆ sample_log_logistic()

◆ sample_log_logistic_scaleshape()

◆ sample_logistic()

◆ sample_logistic_locscale()

◆ sample_uniform_interval()

◆ sample_weibull()

◆ sf_genpareto()

◆ sf_log_logistic()

◆ sf_logistic()

◆ sf_weibull()

◆ uniform_sample()

◆ weibull_sample()

Variable Documentation

◆ genpareto_ops

◆ geometric_ops

◆ log_logistic_ops

◆ logistic_ops

◆ uniform_ops

◆ weibull_ops