LRnexp.c

/*!
\file	LRnexp.c
\brief 	The negative-exponential distribution has mean \e m and deviation \e m.

The pseudo-random numbers are distributed from a negative exponential
distribution.  It's only defined on interval \f$ x \ge 0 \f$ and zero otherwise.
This distribution typically represents the time between events of a
Poisson point process, \e i.e. a process in which events occur continuously
and independently at a constant average rate.

\manonly
   PDF(x) = 1/m * exp(-x/m)
   CDF(x) = 1 - exp(-x/m)
\endmanonly

\f{eqnarray*}{
\mbox{PDF}(x) &=
\left\{ \begin{array}{ll}
                0, &    x < 0 \\
        	\frac{1}{m} e^{-\frac{x}{m}}, &    0 \le x .
        \end{array} \right.
\\
\\
\mbox{CDF}(x) &=
\left\{ \begin{array}{ll}
                0, &    x < 0 \\
        	1 - e^{-\frac{x}{m}}, &    0 \le x .
        \end{array} \right.
\f}


The default is \f$ m = 1 \f$ and \em s will be set to \f$ 1/m \f$
for calculation efficiency.
Do not set \e s when declaring this distribution.
 
*/
/*
 * Copyright	2019	R.K. Owen, Ph.D.
 * License	see lgpl.md (Gnu Lesser General Public License)
 */
#ifdef __cplusplus
extern "C" {
#endif

#include <math.h>
#include "libran.h"

/* double */
/*!
@brief	LRd_nexp_RAN(LR_obj *o) - double random negative exponential
distribution using the inversion method.
Default values: peak m = 1.

@param o        LR_obj object
@return double
*/
double LRd_nexp_RAN(LR_obj *o) {
	double u, zero = 0.0, one = 1.0;

	do {
		u = o->ud(o);
	} while (u == zero);

	return - o->m.d*log(u);
}

/*!
@brief	LRd_nexp_PDF(LR_obj *o, double x) - double negative exponential
probablity distribution function

@param o	LR_obj object
@param x	value
@return double PDF at x
*/
double LRd_nexp_PDF(LR_obj *o, double x) {
	double zero = 0.0, one = 1.0;
	if (isnan(o->s.d))
		o->s.d = one/o->m.d;

	if (x < zero)	return zero;

	return o->s.d * exp(- o->s.d * x);
}

/*!
@brief	LRd_nexp_CDF(LR_obj *o, double x) - double negative exponential
cumulative distribution function

@param o	LR_obj object
@param x	value
@return double CDF at x
*/
double LRd_nexp_CDF(LR_obj *o, double x) {
	double zero = 0.0, one = 1.0;
	if (isnan(o->s.d))
		o->s.d = one/o->m.d;

	if (x < zero)	return zero;

	return one - exp(- o->s.d * x);
}

/* float */
/*!
@brief	LRf_nexp_RAN(LR_obj *o) - float random negative exponential
distribution using the inversion method.
Default values: peak m = 1.

@param o        LR_obj object
@return float
*/
float LRf_nexp_RAN(LR_obj *o) {
	float u, zero = 0.0, one = 1.0;

	do {
		u = o->uf(o);
	} while (u == zero);

	return - o->m.f*log(u);
}

/*!
@brief	LRf_nexp_PDF(LR_obj *o, float x) - float negative exponential
probablity distribution function

@param o	LR_obj object
@param x	value
@return float PDF at x
*/
float LRf_nexp_PDF(LR_obj *o, float x) {
	float zero = 0.0, one = 1.0;
	if (isnan(o->s.f))
		o->s.f = one/o->m.f;

	if (x < zero)	return zero;

	return o->s.f * expf(- o->s.f * x);
}

/*!
@brief	LRf_nexp_CDF(LR_obj *o, float x) - float negative exponential
cumulative distribution function

@param o	LR_obj object
@param x	value
@return float CDF at x
*/
float LRf_nexp_CDF(LR_obj *o, float x) {
	float zero = 0.0, one = 1.0;
	if (isnan(o->s.f))
		o->s.f = one/o->m.f;

	if (x < zero)	return zero;

	return one - expf(- o->s.f * x);
}

#ifdef __cplusplus
}
#endif