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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 Pareto distribution. See ../R/Pareto.R for details.
*
* We work with the density expressed as
*
* shape * u^shape * (1 - u) / x
*
* with u = 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 dpareto(double x, double shape, double scale, int give_log)
{
#ifdef IEEE_754
if (ISNAN(x) || ISNAN(shape) || ISNAN(scale))
return x + shape + scale;
#endif
if (!R_FINITE(shape) ||
shape <= 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) return ACT_D_val(shape / scale);
double logv, logu, log1mu;
logv = log(x) - log(scale);
logu = - log1pexp(logv);
log1mu = - log1pexp(-logv);
return ACT_D_exp(log(shape) + shape * logu + log1mu - log(x));
}
double ppareto(double q, double shape, double scale, int lower_tail, int log_p)
{
#ifdef IEEE_754
if (ISNAN(q) || ISNAN(shape) || ISNAN(scale))
return q + shape + scale;
#endif
if (!R_FINITE(shape) ||
shape <= 0.0 ||
scale <= 0.0)
return R_NaN;
if (q <= 0)
return ACT_DT_0;
double u = exp(-log1pexp(log(q) - log(scale)));
return ACT_DT_Cval(R_pow(u, shape));
}
double qpareto(double p, double shape, double scale, int lower_tail, int log_p)
{
#ifdef IEEE_754
if (ISNAN(p) || ISNAN(shape) || ISNAN(scale))
return p + shape + scale;
#endif
if (!R_FINITE(shape) ||
!R_FINITE(scale) ||
shape <= 0.0 ||
scale <= 0.0)
return R_NaN;
ACT_Q_P01_boundaries(p, 0, R_PosInf);
p = ACT_D_qIv(p);
return scale * (R_pow(ACT_D_Cval(p), -1.0/shape) - 1.0);
}
double rpareto(double shape, double scale)
{
if (!R_FINITE(shape) ||
!R_FINITE(scale) ||
shape <= 0.0 ||
scale <= 0.0)
return R_NaN;
return scale * (R_pow(unif_rand(), -1.0/shape) - 1.0);
}
double mpareto(double order, double shape, double scale, int give_log)
{
#ifdef IEEE_754
if (ISNAN(order) || ISNAN(shape) || ISNAN(scale))
return order + shape + scale;
#endif
if (!R_FINITE(shape) ||
!R_FINITE(scale) ||
!R_FINITE(order) ||
shape <= 0.0 ||
scale <= 0.0)
return R_NaN;
if (order <= -1.0 ||
order >= shape)
return R_PosInf;
return R_pow(scale, order) * gammafn(1.0 + order) * gammafn(shape - order)
/ gammafn(shape);
}
double levpareto(double limit, double shape, double scale, double order,
int give_log)
{
#ifdef IEEE_754
if (ISNAN(limit) || ISNAN(shape) || ISNAN(scale) || ISNAN(order))
return limit + shape + scale + order;
#endif
if (!R_FINITE(shape) ||
!R_FINITE(scale) ||
!R_FINITE(order) ||
shape <= 0.0 ||
scale <= 0.0)
return R_NaN;
if (order <= -1.0)
return R_PosInf;
if (limit <= 0.0)
return 0.0;
double logv, u, u1m;
logv = log(limit) - log(scale);
u = exp(-log1pexp(logv));
u1m = exp(-log1pexp(-logv));
return R_pow(scale, order)
* betaint_raw(u1m, 1.0 + order, shape - order, u)
/ gammafn(shape)
+ ACT_DLIM__0(limit, order) * R_pow(u, shape);
}
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