commit d57300e8ce1154a715b96712898a5564051b9b66
parent 5f1188c5167bd33b46e37c73043644e4aabbe6ca
Author: NunoSempere <nuno.semperelh@protonmail.com>
Date: Sun, 9 Jun 2024 23:01:49 +0200
add implementation for gamma distribution
Diffstat:
1 file changed, 52 insertions(+), 0 deletions(-)
diff --git a/sample/sample.go b/sample/sample.go
@@ -47,6 +47,58 @@ func Sample_to(low float64, high float64, r Src) float64 {
return math.Exp(Sample_normal_from_90_ci(loglow, loghigh, r))
}
+func Sample_gamma(alpha float64, r Src) float64 {
+
+ // a simple method for generating gamma variables, marsaglia and wan tsang, 2001
+ // https://dl.acm.org/doi/pdf/10.1145/358407.358414
+ // see also the references/ folder
+ // note that the wikipedia page for the gamma distribution includes a scaling parameter
+ // k or beta
+ // https://en.wikipedia.org/wiki/gamma_distribution
+ // such that gamma_k(alpha, k) = k * gamma(alpha)
+ // or gamma_beta(alpha, beta) = gamma(alpha) / beta
+ // so far i have not needed to use this, and thus the second parameter is by default 1.
+
+ if alpha >= 1 {
+ var d, c, x, v, u float64
+ d = alpha - 1.0/3.0
+ c = 1.0 / math.Sqrt(9.0*d)
+
+ OuterLoop:
+ for {
+
+ InnerLoop:
+ for {
+ x = Sample_unit_normal(r)
+ v = 1.0 + c*x
+ if v > 0.0 {
+ break InnerLoop
+ }
+ }
+
+ v = v * v * v
+ u = Sample_unit_uniform(r)
+
+ if u < 1.0-0.0331*(x*x*x*x) { // Condition 1
+ // the 0.0331 doesn't inspire much confidence
+ // however, this isn't the whole story
+ // by knowing that Condition 1 implies condition 2
+ // we realize that this is just a way of making the algorithm faster
+ // i.e., of not using the logarithms
+ return d * v
+ }
+ if math.Log(u) < 0.5*(x*x)+d*(1.0-v+math.Log(v)) { // Condition 2
+ return d * v
+ }
+
+ }
+
+ } else {
+ return Sample_gamma(1.0+alpha, r) * math.Pow(Sample_unit_uniform(r), 1.0/alpha)
+ }
+
+}
+
func Sample_mixture(fs []func64, weights []float64, r Src) float64 {
// fmt.Println("weights initially: ", weights)
