simulate range sizes with a log-normal path size distribution

sim.go

package main

import (
	"fmt"
	"math"
	"time"

	"golang.org/x/exp/rand"

	"gonum.org/v1/gonum/stat/distuv"
)

// trial runs a single trial of sampling a value X from rv and using r to stop with probabilty
// t/X.
func trial(r *rand.Rand, rv func() float64, t float64) int {
	for i := 1; ; i++ {
		x := rv()
		if r.Float64() < t/x {
			return i
		}
	}
}

// expected estimates the expected value of trial.
func expected(trialer func() int) float64 {
	const n = 50000
	sum := 0
	for i := 0; i < n; i++ {
		sum += trialer()
	}
	return float64(sum) / float64(n)
}

func main() {
	// estimate the expected value of a stopping time
	source := rand.NewSource(uint64(time.Now().UnixNano()))
	n := &distuv.LogNormal{
		Mu:    7.0,
		Sigma: 2,
		Src:   source,
	}
	r := rand.New(source)
	num := expected(func() int {
		return trial(r, n.Rand, 1)
	})
	fmt.Println("stop: ", num)

	avg := expected(func() int {
		return int(math.Ceil(n.Rand()))
	})
	fmt.Println("value: ", avg)

	fmt.Println("total size: ", num*avg)
}