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#include <Rcpp.h>
#include "shared.h"
// [[Rcpp::interfaces(r, cpp)]]
// [[Rcpp::plugins(cpp11)]]
using std::pow;
using std::sqrt;
using std::abs;
using std::exp;
using std::log;
using std::floor;
using std::ceil;
using Rcpp::NumericVector;
using std::log1p;
/*
* Kumaraswamy distribution
*
* Values:
* x in [0, 1]
*
* Parameters:
* a > 0
* b > 0
*
* f(x) = a*b*x^{a-1}*(1-x^a)^{b-1}
* F(x) = 1-(1-x^a)^b
* F^-1(p) = 1-(1-p^{1/b})^{1/a}
*
*/
inline double pdf_kumar(double x, double a, double b,
bool& throw_warning) {
#ifdef IEEE_754
if (ISNAN(x) || ISNAN(a) || ISNAN(b))
return x+a+b;
#endif
if (a <= 0.0 || b <= 0.0) {
throw_warning = true;
return NAN;
}
if (x < 0.0 || x > 1.0)
return 0.0;
// is the support [0,1] or (0,1) ?
// log(a) + log(b) + log(x)*(a-1.0) + log1p(-pow(x, a))*(b-1.0);
return a*b * pow(x, a-1.0) * pow(1.0-pow(x, a), b-1.0);
}
inline double cdf_kumar(double x, double a, double b,
bool& throw_warning) {
#ifdef IEEE_754
if (ISNAN(x) || ISNAN(a) || ISNAN(b))
return x+a+b;
#endif
if (a <= 0.0 || b <= 0.0) {
throw_warning = true;
return NAN;
}
if (x < 0.0)
return 0.0;
if (x >= 1.0)
return 1.0;
return 1.0 - pow(1.0 - pow(x, a), b);
}
inline double invcdf_kumar(double p, double a, double b,
bool& throw_warning) {
#ifdef IEEE_754
if (ISNAN(p) || ISNAN(a) || ISNAN(b))
return p+a+b;
#endif
if (a <= 0.0 || b <= 0.0 || !VALID_PROB(p)) {
throw_warning = true;
return NAN;
}
return pow(1.0 - pow(1.0 - p, 1.0/b), 1.0/a);
}
inline double rng_kumar(double a, double b, bool& throw_warning) {
if (ISNAN(a) || ISNAN(b) || a <= 0.0 || b <= 0.0) {
throw_warning = true;
return NA_REAL;
}
double u = rng_unif();
return pow(1.0 - pow(u, 1.0/b), 1.0/a);
}
// [[Rcpp::export]]
NumericVector cpp_dkumar(
const NumericVector& x,
const NumericVector& a,
const NumericVector& b,
const bool& log_prob = false
) {
if (std::min({x.length(), a.length(), b.length()}) < 1) {
return NumericVector(0);
}
int Nmax = std::max({
x.length(),
a.length(),
b.length()
});
NumericVector p(Nmax);
bool throw_warning = false;
for (int i = 0; i < Nmax; i++)
p[i] = pdf_kumar(GETV(x, i), GETV(a, i),
GETV(b, i), throw_warning);
if (log_prob)
p = Rcpp::log(p);
if (throw_warning)
Rcpp::warning("NaNs produced");
return p;
}
// [[Rcpp::export]]
NumericVector cpp_pkumar(
const NumericVector& x,
const NumericVector& a,
const NumericVector& b,
const bool& lower_tail = true,
const bool& log_prob = false
) {
if (std::min({x.length(), a.length(), b.length()}) < 1) {
return NumericVector(0);
}
int Nmax = std::max({
x.length(),
a.length(),
b.length()
});
NumericVector p(Nmax);
bool throw_warning = false;
for (int i = 0; i < Nmax; i++)
p[i] = cdf_kumar(GETV(x, i), GETV(a, i),
GETV(b, i), throw_warning);
if (!lower_tail)
p = 1.0 - p;
if (log_prob)
p = Rcpp::log(p);
if (throw_warning)
Rcpp::warning("NaNs produced");
return p;
}
// [[Rcpp::export]]
NumericVector cpp_qkumar(
const NumericVector& p,
const NumericVector& a,
const NumericVector& b,
const bool& lower_tail = true,
const bool& log_prob = false
) {
if (std::min({p.length(), a.length(), b.length()}) < 1) {
return NumericVector(0);
}
int Nmax = std::max({
p.length(),
a.length(),
b.length()
});
NumericVector q(Nmax);
NumericVector pp = Rcpp::clone(p);
bool throw_warning = false;
if (log_prob)
pp = Rcpp::exp(pp);
if (!lower_tail)
pp = 1.0 - pp;
for (int i = 0; i < Nmax; i++)
q[i] = invcdf_kumar(GETV(pp, i), GETV(a, i),
GETV(b, i), throw_warning);
if (throw_warning)
Rcpp::warning("NaNs produced");
return q;
}
// [[Rcpp::export]]
NumericVector cpp_rkumar(
const int& n,
const NumericVector& a,
const NumericVector& b
) {
if (std::min({a.length(), b.length()}) < 1) {
Rcpp::warning("NAs produced");
return NumericVector(n, NA_REAL);
}
NumericVector x(n);
bool throw_warning = false;
for (int i = 0; i < n; i++)
x[i] = rng_kumar(GETV(a, i), GETV(b, i),
throw_warning);
if (throw_warning)
Rcpp::warning("NAs produced");
return x;
}
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