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/* actuar: Actuarial Functions and Heavy Tailed Distributions
*
* Functions to compute density, cumulative distribution and quantile
* functions, raw and limited moments and to simulate random variates
* for the Gumbel distribution. See ../R/Gumbel.R for
* details.
*
* We work with the density expressed as
*
* e^(-u) * e^(-e^(-u)) / scale
*
* with u = (x - alpha)/scale.
*
* AUTHOR: Vincent Goulet <vincent.goulet@act.ulaval.ca>
*/
#include <R.h>
#include <Rmath.h>
#include "locale.h"
#include "dpq.h"
double dgumbel(double x, double alpha, double scale, int give_log)
{
#ifdef IEEE_754
if (ISNAN(x) || ISNAN(alpha) || ISNAN(scale))
return x + alpha + scale;
#endif
if (!R_FINITE(scale))
return ACT_D__0;
if (!R_FINITE(x) && alpha == x)
return R_NaN; /* x - alpha is NaN */
if (scale <= 0)
{
if (scale < 0) return R_NaN;
/* scale == 0 */
return (x == alpha) ? R_PosInf : ACT_D__0;
}
x = (x - alpha) / scale;
if (!R_FINITE(x))
return ACT_D__0;
return ACT_D_exp(-(x + exp(-x) + log(scale)));
}
double pgumbel(double q, double alpha, double scale, int lower_tail,
int log_p)
{
#ifdef IEEE_754
if (ISNAN(q) || ISNAN(alpha) || ISNAN(scale))
return q + alpha + scale;
#endif
if (!R_FINITE(q) && alpha == q)
return R_NaN; /* q - alpha is NaN */
if (scale <= 0)
{
if (scale < 0) return R_NaN;
/* scale == 0 : */
return (q < alpha) ? ACT_DT_0 : ACT_DT_1;
}
double p = (q - alpha) / scale;
if (!R_FINITE(p))
return (q < alpha) ? ACT_DT_0 : ACT_DT_1;
q = p;
return ACT_DT_val(exp(-exp(-q)));
}
double qgumbel(double p, double alpha, double scale, int lower_tail,
int log_p)
{
#ifdef IEEE_754
if (ISNAN(p) || ISNAN(alpha) || ISNAN(scale))
return p + alpha + scale;
#endif
if (!R_FINITE(alpha) ||
!R_FINITE(scale) ||
scale <= 0.0)
return R_NaN;;
ACT_Q_P01_boundaries(p, R_NegInf, R_PosInf);
p = ACT_DT_qIv(p);
return alpha - scale * log(-log(p));
}
double rgumbel(double alpha, double scale)
{
if (!R_FINITE(alpha) ||
!R_FINITE(scale) ||
scale <= 0.0)
return R_NaN;;
return alpha - scale * log(exp_rand());
}
#define EULER_CNST 0.577215664901532860606512090082
double mgumbel(double order, double alpha, double scale, int give_log)
{
#ifdef IEEE_754
if (ISNAN(order) || ISNAN(alpha) || ISNAN(scale))
return order + alpha + scale;
#endif
if (!R_FINITE(alpha) ||
!R_FINITE(scale) ||
!R_FINITE(order) ||
scale <= 0.0 ||
order <= 0.0 ||
order > 2.0)
return R_NaN;
if (order == 1.0)
return alpha + EULER_CNST * scale;
if (order == 2.0)
return R_pow_di(M_PI * scale, 2)/6 + R_pow_di(alpha + EULER_CNST * scale, 2);
return R_NaN; /* order != 1 or 2 */
}
double mgfgumbel(double t, double alpha, double scale, int give_log)
{
#ifdef IEEE_754
if (ISNAN(t) || ISNAN(alpha) || ISNAN(scale))
return t + alpha + scale;
#endif
if (!R_FINITE(alpha) ||
!R_FINITE(scale) ||
scale <= 0.0 ||
scale * t < 1.0)
return R_NaN;
if (t == 0.0)
return ACT_D__1;
return ACT_D_exp(alpha * t + lgamma(1 - scale * t));
}
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