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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 inverse paralogistic distribution. See ../R/InverseParalogistic.R
* for details.
*
* We work with the density expressed as
*
* shape^2 * u^shape * (1 - u) / x
*
* with u = v/(1 + v) = 1/(1 + 1/v), v = (x/scale)^shape.
*
* 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 dinvparalogis(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)
{
if (shape < 1.0) return R_PosInf;
if (shape > 1.0) return ACT_D__0;
/* else */
return ACT_D_val(1.0/scale);
}
double logv, logu, log1mu;
logv = shape * (log(x) - log(scale));
logu = - log1pexp(-logv);
log1mu = - log1pexp(logv);
return ACT_D_exp(2.0 * log(shape) + shape * logu + log1mu - log(x));
}
double pinvparalogis(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(shape * (log(scale) - log(q))));
return ACT_DT_val(R_pow(u, shape));
}
double qinvparalogis(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);
double tmp = -1.0/shape;
return scale * R_pow(R_pow(ACT_D_Lval(p), tmp) - 1.0, tmp);
}
double rinvparalogis(double shape, double scale)
{
double tmp;
if (!R_FINITE(shape) ||
!R_FINITE(scale) ||
shape <= 0.0 ||
scale <= 0.0)
return R_NaN;;
tmp = -1.0/shape;
return scale * R_pow(R_pow(unif_rand(), tmp) - 1.0, tmp);
}
double minvparalogis(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 <= - shape * shape ||
order >= shape)
return R_PosInf;
double tmp = order / shape;
return R_pow(scale, order) * gammafn(shape + tmp) * gammafn(1.0 - tmp)
/ gammafn(shape);
}
double levinvparalogis(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 <= -shape * shape)
return R_PosInf;
double logv, u, u1m;
double tmp = order / shape;
logv = shape * (log(limit) - log(scale));
u = exp(-log1pexp(-logv));
u1m = exp(-log1pexp(logv));
return R_pow(scale, order)
* betaint_raw(u, shape + tmp, 1.0 - tmp, u1m)
/ gammafn(shape)
+ ACT_DLIM__0(limit, order) * (0.5 - R_pow(u, shape) + 0.5);
}
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