Esempio n. 1
0
func Example() {
	fmt.Println("Evaluate the expected value of x^2 + 3 under a Weibull distribution")
	f := func(x float64) float64 {
		d := distuv.Weibull{Lambda: 1, K: 1.5}
		return (x*x + 3) * d.Prob(x)
	}
	ev := quad.Fixed(f, 0, math.Inf(1), 10, nil, 0)
	fmt.Printf("EV with 10 points = %0.6v\n", ev)

	ev = quad.Fixed(f, 0, math.Inf(1), 30, nil, 0)
	fmt.Printf("EV with 30 points = %0.6v\n", ev)

	ev = quad.Fixed(f, 0, math.Inf(1), 100, nil, 0)
	fmt.Printf("EV with 100 points = %0.6v\n", ev)

	ev = quad.Fixed(f, 0, math.Inf(1), 10000, nil, 0)
	fmt.Printf("EV with 10000 points = %0.6v\n\n", ev)

	fmt.Println("Estimate using parallel evaluations of f.")
	concurrent := runtime.GOMAXPROCS(0)
	ev = quad.Fixed(f, 0, math.Inf(1), 100, nil, concurrent)
	fmt.Printf("EV = %0.6v\n", ev)
	// Output:
	// Evaluate the expected value of x^2 + 3 under a Weibull distribution
	// EV with 10 points = 4.20175
	// EV with 30 points = 4.19066
	// EV with 100 points = 4.19064
	// EV with 10000 points = 4.19064
	//
	// Estimate using parallel evaluations of f.
	// EV = 4.19064
}
Esempio n. 2
0
func checkProbContinuous(t *testing.T, i int, x []float64, p probLogprober) {
	// Check that the PDF is consistent (integrates to 1).
	q := quad.Fixed(p.Prob, math.Inf(-1), math.Inf(1), 100000, nil, 0)
	if math.Abs(q-1) > 1e-10 {
		t.Errorf("Probability distribution doesn't integrate to 1. Got %v", q)
	}

	// Check that PDF and LogPDF are consistent.
	for i, v := range x {
		if math.Abs(math.Log(p.Prob(v))-p.LogProb(v)) > 1e-14 {
			t.Errorf("Prob and LogProb mismatch case %v at %v: want %v, got %v", i, v, math.Log(v), p.LogProb(v))
			break
		}
	}
}
Esempio n. 3
0
// checkProbQuantContinuous checks that the Prob, Rand, and Quantile are all consistent.
// checkProbContinuous only checks that Prob is a valid distribution (integrates
// to 1 and greater than 0). However, this is also true if the PDF of a different
// distribution is used. This checks that PDF is also consistent with the
// CDF implementation and the random samples.
func checkProbQuantContinuous(t *testing.T, i int, xs []float64, c cumulantProber, tol float64) {
	ps := make([]float64, 101)
	floats.Span(ps, 0, 1)

	var xp, x float64
	for i, p := range ps {
		x = c.Quantile(p)
		if p == 0 {
			xp = x
			if floats.Min(xs) < x {
				t.Errorf("Sample of x less than Quantile(0). Case %v.", i)
				break
			}
			continue
		}
		if p == 1 {
			if floats.Max(xs) > x {
				t.Errorf("Sample of x greater than Quantile(1). Case %v.", i)
				break
			}
		}

		// The integral of the PDF between xp and x should be the difference in
		// the quantiles.
		q := quad.Fixed(c.Prob, xp, x, 1000, nil, 0)
		if math.Abs(q-(p-ps[i-1])) > 1e-10 {
			t.Errorf("Integral of PDF doesn't match quantile. Case %v. Want %v, got %v.", i, p-ps[i-1], q)
			break
		}

		pEst := stat.CDF(x, stat.Empirical, xs, nil)
		if math.Abs(pEst-p) > tol {
			t.Errorf("Empirical CDF doesn't match quantile. Case %v.", i)
		}
		xp = x
	}
}