expgrowth.stan

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real expgrowth_pdf(real x, real xmin, real xmax, real r) {
  if (x < xmin || x > xmax) {
    return 0;
  }
  if (abs(r) < 1e-10) {
    return 1 / (xmax - xmin);
  }
  return r * exp(r * x) / (exp(r * xmax) - exp(r * xmin));
}
 
real expgrowth_lpdf(real x, real xmin, real xmax, real r) {
  if (x < xmin || x > xmax) {
    return negative_infinity();
  }
  if (abs(r) < 1e-10) {
    return -log(xmax - xmin);
  }
  return log(abs(r)) + r * x -
    log(abs(exp(r * xmax) - exp(r * xmin)));
}
 
real expgrowth_cdf(real x, real xmin, real xmax, real r) {
  if (x < xmin) {
    return 0;
  }
  if (x > xmax) {
    return 1;
  }
  if (abs(r) < 1e-10) {
    return (x - xmin) / (xmax - xmin);
  }
  return (exp(r * x) - exp(r * xmin)) / (exp(r * xmax) - exp(r * xmin));
}
 
real expgrowth_lcdf(real x, real xmin, real xmax, real r) {
  if (x < xmin) {
    return negative_infinity();
  }
  if (x > xmax) {
    return 0;
  }
  return log(expgrowth_cdf(x | xmin, xmax, r));
}
 
real expgrowth_rng(real xmin, real xmax, real r) {
  real u = uniform_rng(0, 1);
  if (abs(r) < 1e-10) {
    return xmin + u * (xmax - xmin);
  }
  return log(u * exp(r * xmax) + (1 - u) * exp(r * xmin)) / r;
}