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 // Copyright ©2017 The Gonum Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. package distuv import ( "math" "sort" "testing" "golang.org/x/exp/rand" "gonum.org/v1/gonum/floats/scalar" ) func TestParetoProb(t *testing.T) { t.Parallel() for _, test := range []struct { x, xm, alpha, want float64 }{ {0, 1, 1, 0}, {0.5, 1, 1, 0}, {1, 1, 1, 1.0}, {1.5, 1, 1, 0.444444444444444}, {2, 1, 1, 0.25}, {2.5, 1, 1, 0.16}, {3, 1, 1, 0.1111111111111111}, {3.5, 1, 1, 0.081632653061224}, {4, 1, 1, 0.0625}, {4.5, 1, 1, 0.049382716049383}, {5, 1, 1, 0.04}, {0, 1, 2, 0}, {0.5, 1, 2, 0}, {1, 1, 2, 2}, {1.5, 1, 2, 0.592592592592593}, {2, 1, 2, 0.25}, {2.5, 1, 2, 0.128}, {3, 1, 2, 0.074074074074074}, {3.5, 1, 2, 0.046647230320700}, {4, 1, 2, 0.03125}, {4.5, 1, 2, 0.021947873799726}, {5, 1, 2, 0.016}, {0, 1, 3, 0}, {0.5, 1, 3, 0}, {1, 1, 3, 3.0}, {1.5, 1, 3, 0.592592592592593}, {2, 1, 3, 0.1875}, {2.5, 1, 3, 0.0768}, {3, 1, 3, 0.037037037037037}, {3.5, 1, 3, 0.019991670137443}, {4, 1, 3, 0.011718750000000}, {4.5, 1, 3, 0.007315957933242}, {5, 1, 3, 0.0048}, } { pdf := Pareto{test.xm, test.alpha, nil}.Prob(test.x) if !scalar.EqualWithinAbsOrRel(pdf, test.want, 1e-10, 1e-10) { t.Errorf("Pdf mismatch, x = %v, xm = %v, alpha = %v. Got %v, want %v", test.x, test.xm, test.alpha, pdf, test.want) } } } func TestParetoCDF(t *testing.T) { t.Parallel() for _, test := range []struct { x, xm, alpha, want float64 }{ {0, 1, 1, 0}, {0.5, 1, 1, 0}, {1, 1, 1, 0}, {1.5, 1, 1, 0.333333333333333}, {2, 1, 1, 0.5}, {2.5, 1, 1, 0.6}, {3, 1, 1, 0.666666666666667}, {3.5, 1, 1, 0.714285714285714}, {4, 1, 1, 0.75}, {4.5, 1, 1, 0.777777777777778}, {5, 1, 1, 0.80}, {5.5, 1, 1, 0.818181818181818}, {6, 1, 1, 0.833333333333333}, {6.5, 1, 1, 0.846153846153846}, {7, 1, 1, 0.857142857142857}, {7.5, 1, 1, 0.866666666666667}, {8, 1, 1, 0.875}, {8.5, 1, 1, 0.882352941176471}, {9, 1, 1, 0.888888888888889}, {9.5, 1, 1, 0.894736842105263}, {10, 1, 1, 0.90}, {0, 1, 2, 0}, {0.5, 1, 2, 0}, {1, 1, 2, 0}, {1.5, 1, 2, 0.555555555555556}, {2, 1, 2, 0.75}, {2.5, 1, 2, 0.84}, {3, 1, 2, 0.888888888888889}, {3.5, 1, 2, 0.918367346938776}, {4, 1, 2, 0.9375}, {4.5, 1, 2, 0.950617283950617}, {5, 1, 2, 0.96}, {5.5, 1, 2, 0.966942148760331}, {6, 1, 2, 0.972222222222222}, {6.5, 1, 2, 0.976331360946746}, {7, 1, 2, 0.979591836734694}, {7.5, 1, 2, 0.982222222222222}, {8, 1, 2, 0.984375000000000}, {8.5, 1, 2, 0.986159169550173}, {9, 1, 2, 0.987654320987654}, {9.5, 1, 2, 0.988919667590028}, {10, 1, 2, 0.99}, {0, 1, 3, 0}, {0.5, 1, 3, 0}, {1, 1, 3, 0}, {1.5, 1, 3, 0.703703703703704}, {2, 1, 3, 0.875}, {2.5, 1, 3, 0.936}, {3, 1, 3, 0.962962962962963}, {3.5, 1, 3, 0.976676384839650}, {4, 1, 3, 0.984375000000000}, {4.5, 1, 3, 0.989026063100137}, {5, 1, 3, 0.992}, {5.5, 1, 3, 0.993989481592787}, {6, 1, 3, 0.995370370370370}, {6.5, 1, 3, 0.996358670914884}, {7, 1, 3, 0.997084548104956}, {7.5, 1, 3, 0.997629629629630}, {8, 1, 3, 0.998046875000000}, {8.5, 1, 3, 0.998371667005903}, {9, 1, 3, 0.998628257887517}, {9.5, 1, 3, 0.998833649220003}, {10, 1, 3, 0.999}, } { cdf := Pareto{test.xm, test.alpha, nil}.CDF(test.x) if !scalar.EqualWithinAbsOrRel(cdf, test.want, 1e-10, 1e-10) { t.Errorf("CDF mismatch, x = %v, xm = %v, alpha = %v. Got %v, want %v", test.x, test.xm, test.alpha, cdf, test.want) } } } func TestPareto(t *testing.T) { t.Parallel() src := rand.New(rand.NewSource(1)) for i, p := range []Pareto{ {1, 10, src}, {1, 20, src}, } { testPareto(t, p, i) } } func testPareto(t *testing.T, p Pareto, i int) { const ( tol = 1e-2 n = 1e6 bins = 50 ) x := make([]float64, n) generateSamples(x, p) sort.Float64s(x) checkQuantileCDFSurvival(t, i, x, p, 1e-3) testRandLogProbContinuous(t, i, 0, x, p, tol, bins) checkMean(t, i, x, p, tol) checkVarAndStd(t, i, x, p, tol) checkExKurtosis(t, i, x, p, 7e-2) checkProbContinuous(t, i, x, p.Xm, math.Inf(1), p, 1e-10) checkEntropy(t, i, x, p, 1e-2) checkMedian(t, i, x, p, 1e-3) if p.Xm != p.Mode() { t.Errorf("Mismatch in mode value: got %v, want %g", p.Mode(), p.Xm) } if p.NumParameters() != 2 { t.Errorf("Mismatch in NumParameters: got %v, want 2", p.NumParameters()) } surv := p.Survival(p.Xm - 0.0001) if surv != 1 { t.Errorf("Mismatch in Survival below Xm: got %v, want 1", surv) } } func TestParetoNotExists(t *testing.T) { t.Parallel() p := Pareto{0, 4, nil} exKurt := p.ExKurtosis() if !math.IsNaN(exKurt) { t.Errorf("Expected NaN excess kurtosis for Alpha == 4, got %v", exKurt) } p = Pareto{0, 1, nil} mean := p.Mean() if !math.IsInf(mean, 1) { t.Errorf("Expected mean == +Inf for Alpha == 1, got %v", mean) } p = Pareto{0, 2, nil} variance := p.Variance() if !math.IsInf(variance, 1) { t.Errorf("Expected variance == +Inf for Alpha == 1, got %v", variance) } stdDev := p.StdDev() if !math.IsInf(stdDev, 1) { t.Errorf("Expected standard deviation == +Inf for Alpha == 1, got %v", stdDev) } }