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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 Generalized Pareto distribution.. See ../R/GeneralizedPareto.R
* for details.
*
* We work with the density expressed as
*
* u^shape2 * (1 - u)^shape1 / (x * beta(shape1, shape2))
*
* with u = v/(1 + v) = 1/(1 + 1/v), v = x/scale.
*
* AUTHORS: Mathieu Pigeon and Vincent Goulet <vincent.goulet@act.ulaval.ca>
*/
#include <R.h>
#include <Rmath.h>
#include "locale.h"
#include "dpq.h"
#include "actuar.h"
double dgenpareto(double x, double shape1, double shape2, double scale,
int give_log)
{
#ifdef IEEE_754
if (ISNAN(x) || ISNAN(shape1) || ISNAN(shape2) || ISNAN(scale))
return x + shape1 + shape2 + scale;
#endif
if (!R_FINITE(shape1) ||
!R_FINITE(shape2) ||
shape1 <= 0.0 ||
shape2 <= 0.0 ||
scale <= 0.0)
return R_NaN;
if (!R_FINITE(x) || x < 0.0)
return ACT_D__0;
/* handle x == 0 separately */
if (x == 0.0)
{
if (shape2 < 1) return R_PosInf;
if (shape2 > 1) return ACT_D__0;
/* else */
return give_log ?
- log(scale) - lbeta(shape2, shape1) :
1.0/(scale * beta(shape2, shape1));
}
double logv, logu, log1mu;
logv = log(x) - log(scale);
logu = - log1pexp(-logv);
log1mu = - log1pexp(logv);
return ACT_D_exp(shape2 * logu + shape1 * log1mu - log(x)
- lbeta(shape2, shape1));
}
double pgenpareto(double q, double shape1, double shape2, double scale,
int lower_tail, int log_p)
{
#ifdef IEEE_754
if (ISNAN(q) || ISNAN(shape1) || ISNAN(shape2) || ISNAN(scale))
return q + shape1 + shape2 + scale;
#endif
if (!R_FINITE(shape1) ||
!R_FINITE(shape2) ||
shape1 <= 0.0 ||
shape2 <= 0.0 ||
scale <= 0.0)
return R_NaN;
if (q <= 0)
return ACT_DT_0;
double logvm, u;
logvm = log(scale) - log(q); /* -log v */
u = exp(-log1pexp(logvm));
if (u > 0.5)
{
/* Compute (1 - u) accurately */
double u1m = exp(-log1pexp(-logvm));
return pbeta(u1m, shape1, shape2, 1 - lower_tail, log_p);
}
/* else u <= 0.5 */
return pbeta(u, shape2, shape1, lower_tail, log_p);
}
double qgenpareto(double p, double shape1, double shape2, double scale,
int lower_tail, int log_p)
{
#ifdef IEEE_754
if (ISNAN(p) || ISNAN(shape1) || ISNAN(shape2) || ISNAN(scale))
return p + shape1 + shape2 + scale;
#endif
if (!R_FINITE(shape1) ||
!R_FINITE(shape2) ||
!R_FINITE(scale) ||
shape1 <= 0.0 ||
shape2 <= 0.0 ||
scale <= 0.0)
return R_NaN;
ACT_Q_P01_boundaries(p, 0, R_PosInf);
p = ACT_D_qIv(p);
return scale / (1.0 / qbeta(p, shape2, shape1, lower_tail, 0) - 1.0);
}
double rgenpareto(double shape1, double shape2, double scale)
{
if (!R_FINITE(shape1) ||
!R_FINITE(shape2) ||
!R_FINITE(scale) ||
shape1 <= 0.0 ||
shape2 <= 0.0 ||
scale <= 0.0)
return R_NaN;
return scale / (1.0 / rbeta(shape2, shape1) - 1.0);
}
double mgenpareto(double order, double shape1, double shape2, double scale,
int give_log)
{
#ifdef IEEE_754
if (ISNAN(order) || ISNAN(shape1) || ISNAN(shape2) || ISNAN(scale))
return order + shape1 + shape2 + scale;
#endif
if (!R_FINITE(shape1) ||
!R_FINITE(shape2) ||
!R_FINITE(scale) ||
!R_FINITE(order) ||
shape1 <= 0.0 ||
shape2 <= 0.0 ||
scale <= 0.0)
return R_NaN;
if (order <= -shape2 ||
order >= shape1)
return R_PosInf;
return R_pow(scale, order) * beta(shape1 - order, shape2 + order)
/ beta(shape1, shape2);
}
double levgenpareto(double limit, double shape1, double shape2, double scale,
double order, int give_log)
{
#ifdef IEEE_754
if (ISNAN(limit) || ISNAN(shape1) || ISNAN(shape2) || ISNAN(scale) || ISNAN(order))
return limit + shape1 + shape2 + scale + order;
#endif
if (!R_FINITE(shape1) ||
!R_FINITE(shape2) ||
!R_FINITE(scale) ||
!R_FINITE(order) ||
shape1 <= 0.0 ||
shape2 <= 0.0 ||
scale <= 0.0)
return R_NaN;
if (order <= -shape2)
return R_PosInf;
if (limit <= 0.0)
return 0.0;
double logv, u, u1m, Ix;
logv = log(limit) - log(scale);
u = exp(-log1pexp(-logv));
u1m = exp(-log1pexp(logv));
Ix = (u > 0.5) ?
pbeta(u1m, shape1, shape2, /*l._t.*/1, /*give_log*/0) :
pbeta(u, shape2, shape1, /*l._t.*/0, /*give_log*/0);
return R_pow(scale, order)
* betaint_raw(u, shape2 + order, shape1 - order, u1m)
/ (gammafn(shape1) * gammafn(shape2))
+ ACT_DLIM__0(limit, order) * Ix;
}
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