tweedie_logW.cpp

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// Re-structured version of tweedie density function from 'cplm' package.

/* the threshold used in finding the bounds of the series */
#define TWEEDIE_DROP 37.0
/* the loop increment used in finding the bounds of the series */
#define TWEEDIE_INCRE 5
/* the max number of terms allowed in the finite sum approximation*/
#define TWEEDIE_NTERM 20000

template<class Float>
Float tweedie_logW(double y, Float& phi, Float& p){
  bool ok = (0 < y) && (0 < phi) && (1 < p) && (p < 2);
  if (!ok) return NAN;

  Float p1 = p - 1.0, p2 = 2.0 - p;
  Float a = - p2 / p1, a1 = 1.0 / p1;
  Float cc, w, sum_ww = 0.0;
  double ww_max = -INFINITY ;

  /* only need the lower bound and the # terms to be stored */
  double jmax = 0;
  Float logz = 0;

  /* compute jmax for the given y > 0*/
  cc = a * log(p1) - log(p2);
  jmax = asDouble( fmax2(1.0, pow(y, p2) / (phi * p2)) );
  logz = - a * log(y) - a1 * log(phi) + cc;

  /* find bounds in the summation */
  /* locate upper bound */
  cc = logz + a1 + a * log(-a);
  double j = jmax ;
  w = a1 * j ;
  while (1) {
    j += TWEEDIE_INCRE ;
    if (j * (cc - a1 * log(j)) < (w - TWEEDIE_DROP))
      break ;
  }
  int jh = static_cast<int>(ceil(j));
  /* locate lower bound */
  j = jmax;
  while (1) {
    j -= TWEEDIE_INCRE ;
    if (j < 1 || j * (cc - a1 * log(j)) < w - TWEEDIE_DROP)
      break ;
  }
  int jl = imax2(1, floor(j)) ;
  int jd = jh - jl + 1;

  /* set limit for # terms in the sum */
  int nterms = imin2(jd, TWEEDIE_NTERM) ;
  //std::vector<Float> ww(nterms);
  /* evaluate series using the finite sum*/
  /* y > 0 */
  sum_ww = 0.0 ;
  int iterm = imin2(jd, nterms) ;
  std::vector<Float> ww(iterm);
  for (int k = 0; k < iterm; k++) {
    j = k + jl ;
    ww[k] = j * logz - lgamma(1 + j) - lgamma(-a * j);
    ww_max = fmax2( ww_max, asDouble(ww[k]) );
  }
  for (int k = 0; k < iterm; k++)
    sum_ww += exp(ww[k] - ww_max);
  Float ans = log(sum_ww) + ww_max  ;

  return ans;
}