double dinvparalogis(double x, double shape, double scale, int give_log)
{
/* 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.
*/
double tmp, logu, log1mu;
if (!R_FINITE(shape) ||
!R_FINITE(scale) ||
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)
{
if (shape < 1.0) return R_PosInf;
if (shape > 1.0) return ACT_D__0;
/* else */
return ACT_D_val(1.0 / scale);
}
tmp = shape * (log(x) - log(scale));
logu = - log1pexp(-tmp);
log1mu = - log1pexp(tmp);
return ACT_D_exp(2.0 * log(shape) + shape * logu + log1mu - log(x));
}
double dztgeom(double x, double prob, int give_log)
{
#ifdef IEEE_754
if (ISNAN(x) || ISNAN(prob))
return x + prob;
#endif
if (prob <= 0 || prob > 1) return R_NaN;
if (x < 1 || !R_FINITE(x)) return ACT_D__0;
/* limiting case as prob approaches one is point mass at one */
if (prob == 1) return (x == 1) ? ACT_D__1 : ACT_D__0;
return ACT_D_val(dgeom(x - 1, prob, /*give_log*/0));
}
double dztbinom(double x, double size, double prob, int give_log)
{
/* We compute Pr[X = 0] with dbinom_raw() [as would eventually
* dbinom()] to take advantage of all the optimizations for
* small/large values of 'prob' and 'size' (and also to skip some
* validity tests).
*/
#ifdef IEEE_754
if (ISNAN(x) || ISNAN(size) || ISNAN(prob))
return x + size + prob;
#endif
if (prob < 0 || prob > 1 || size < 1) return R_NaN;
if (x < 1 || !R_FINITE(x)) return ACT_D__0;
/* limiting cases as size -> 1 or prob -> 0 are point mass at one */
if (size == 1 || prob == 0) return (x == 1) ? ACT_D__1 : ACT_D__0;
double lp0 = dbinom_raw(0, size, prob, 1 - prob, /*give_log*/1);
return ACT_D_val(dbinom(x, size, prob, /*give_log*/0)/(-expm1(lp0)));
}