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QQ图

QQ图
几何画板及绘图内容加载中，请稍等……
2015-08-09 11:46
函数概率统计变换
该范例演示了QQ图，这是一种用于比较两个数据集分布的图形方法。核心数学概念包括概率统计中的正态分布、伽马分布和指数分布。通过使用GeoGebra命令如RandomUniform、Sort、Mirror等，可以构造QQ图来直观地比较不同分布的数据集。适合高中及以上学生或统计学爱好者学习和研究。

GeoGebra 命令及参数

  1. SelectedIndex(distributionsmodel) → SelectedModel
  2. SelectedIndex(distributionsreal) → SelectedReal
  3. RandomUniform(0, 1, n) → samplereal
  4. Zip((-9, InverseNormal[μ, σ, yy]), yy, samplereal) → pointsrealNormal
  5. Zip((-9, InverseGamma[3, β, yy] - 2), yy, samplereal) → pointsrealGamma
  6. Zip((-9, InverseExponential[λ, yy] - 2), yy, samplereal) → pointsrealExp
  7. Zip((-9, InverseGamma[s / 2, 2, yy]), yy, samplereal) → pointsreal2
  8. Zip((-9, ((-yy) + s) / sqrt((2 * s)) + 2.5), yy, y(pointsreal2)) → pointsrealSkewLeft
  9. Zip((-9, (yy - s) / sqrt((2 * s))), yy, y(pointsreal2)) → pointsrealSkewRight
  10. If(SelectedReal ≟ 1, pointsrealNormal, If[SelectedReal ≟ 2, pointsrealExp, If[SelectedReal ≟ 3, pointsrealGamma, If[SelectedReal ≟ 4, pointsrealSkewRight, pointsrealSkewLeft]]]) → pointsReal
  11. Sort(y(pointsReal)) → ysortReal
  12. Sequence(k / (n + 1), k, 1, n, 1) → points
  13. Zip((InverseNormal[μ_M, σ_M, yy] - 3, 2.2), yy, points) → pointsmodelNorm
  14. Zip((InverseGamma[3, β_M, yy] - 7, 2.2), yy, points) → pointsmodelGamma
  15. Zip((InverseExponential[λ_M, yy] - 7, 2.2), yy, points) → pointsmodelExp
  16. Zip((InverseGamma[s_M / 2, 2, yy], 2.2), yy, points) → pointsmodel2
  17. Zip(((yy - s_M) / sqrt((2 * s_M)) - 3, 2.2), yy, x(pointsmodel2)) → pointsmodelSkewRight
  18. Mirror(pointsmodelSkewRight, x = -3) → pointsmodelSkewLeft
  19. If(SelectedModel ≟ 1, pointsmodelNorm, If[SelectedModel ≟ 2, pointsmodelExp, If[SelectedModel ≟ 3, pointsmodelGamma, If[SelectedModel ≟ 4, pointsmodelSkewRight, pointsmodelSkewLeft]]]) → pointsModel
  20. Sort(x(pointsModel)) → xsortModel
  21. If(SelectedReal ≟ 1, pointsrealNormal, If[SelectedReal ≟ 2, pointsrealExp, If[SelectedReal ≟ 3, pointsrealGamma, If[SelectedReal ≟ 4, pointsrealSkewRight, pointsrealSkewLeft]]]) → points1
  22. Sort(y(points1)) → points3
  23. Zip((InverseExponential[λ_M, yy] - 7, xx), yy, points, xx, points3) → Fexp
  24. Zip((InverseGamma[3, β_M, yy] - 7, xx), yy, points, xx, points3) → Fgamma
  25. Zip((x(xx), yy), xx, pointsModel, yy, points3) → FSkewRight
  26. Zip((x(xx), yy), xx, pointsModel, yy, points3) → FSkewLeftaux
  27. Zip((xx, yy), xx, xsortModel, yy, ysortReal) → FSkewLeft
  28. Zip((InverseNormal[μ_M, σ_M, yy] - 3, xx), yy, points, xx, points3) → Fnorm
  29. Gamma(s_M / 2, 2, x) → g_M
  30. Gamma(s / 2, 2, x) → g
  31. Gamma(3, β_M, x) → GammaModel
  32. Normal(μ_M, σ_M, x) → NormalModel
  33. Exponential(λ_M, x) → ExpModel
  34. Gamma(3, β, x) → GammaReal
  35. Exponential(λ, x) → ExpReal
  36. Normal(μ, σ, x) → NormalReal
  37. If(SelectedReal ≟ 1, σ, If[SelectedReal ≟ 2, 1 / λ^(2), 3 / β^(2)]) → varReal
  38. If(SelectedReal ≟ 1, μ, If[SelectedReal ≟ 2, 1 / λ, 3 / β]) → meanReal
  39. Element(rulesreal, SelectedReal) → freal
  40. Sort(samplereal) → samplerealord
  41. Element(rulesmodel, SelectedModel) → fmodel
  42. Q1(xpointsModel) → q1Model
  43. Q3(xpointsModel) → q3Model
  44. If(SelectedModel ≟ 1, μ_M, If[SelectedModel ≟ 2, 1 / λ_M, 3 / β_M]) → meanModel
  45. If(SelectedModel ≟ 1, σ_M, If[SelectedModel ≟ 2, 1 / λ_M^(2), 3 / β_M^(2)]) → varModel
  46. Max(x(pointsModel)) → xMaxpointsModel
  47. Translate(Rotate[frealrestrict, 1.5708], (-10, 0)) → gNormSkew
  48. Segment((-10, -2.5), (-10, 5)) → RealpdfAxis
  49. Segment((-9, -2.5), (-9, 5)) → RealsampleAxis
  50. Sequence(Text[i, (-7.9, i - 0.1)], i, -2, 5) → listyyNormSkewRight
  51. Sequence(Text[i, (i - 3.1, -2.9)], i, -4, 4) → listxxNormSkew
  52. Sequence(Text[i, (-7.9, i - 2.1)], i, 0, 7) → listyyExpGamma
  53. Translate(Rotate[frealrestrict, 1.5708], (-10, -2)) → gExpGamma
  54. Segment((-7.5, 2.2), (1.5, 2.2)) → modelaxis
  55. If(SelectedModel ≟ 1, Fnorm, If[SelectedModel ≟ 2, Fexp, If[SelectedModel ≟ 3, Fgamma, If[SelectedModel ≟ 4, FSkewRight, FSkewLeft]]]) → QQpoints
  56. Element(QQpoints, 2) → Min2QQ
  57. Element(pointsModel, 2) → Min2Model
  58. Element(pointsModel, n - 1) → MaxModel
  59. Polygon((x(Corner[1]) + 4.5, y(Corner[1]) + 0.8), (x(Corner[1]), y(Corner[1]) + 0.8), (x(Corner[1]), y(Corner[1])), (x(Corner[1]) + 4.5, y(Corner[1]))) → bottombar, k, l, m, p
  60. Segment(Min2Real, Min2QQ) → A
  61. Segment(Min2QQ, (x(Min2QQ), -4)) → D
  62. Polygon((x(Corner[4]), y(Corner[4])), (x(Corner[4]) + 4.6, y(Corner[4])), (x(Corner[4]) + 4.6, y(Corner[4]) - 0.7), (x(Corner[4]), y(Corner[4]) - 0.7)) → topbar, a_1, c, d, e
  63. Normal(0, 1, x) → Snorm
  64. Polygon((x(Corner[2]) - 5.5, y(Corner[2])), Corner[2], Corner[3] + 1, (x(Corner[3]) - 5.5, y(Corner[3]) + 1)) → sidebar, a, f, h, i
  65. Gamma(s / 2, 0.5, sqrt((2 * s)) + s) → b
  66. Zip(InverseGamma[s / 2, 2, yy], yy, samplereal) → Skewpoints
  67. Sequence(Text[i, (i - 7.1, -2.9)], i, 0, 8) → listxxExpGamma
  68. Segment((-7.5, 0), (1.5, 0)) → xaxisbottom
  69. Sequence(Segment[Element[pointsModel, i], (x(Element[pointsModel, i]), 0)], i, 1, n) → LinesModel
  70. Element(QQpoints, n - 1) → Max2QQ
  71. Segment(Max2Real, Max2QQ) → B
  72. Segment(Max2QQ, (x(Max2QQ), -4)) → E
  73. Segment((x(MaxModel), 3), (x(MaxModel), 2.2)) → L
  74. Segment((x(Min2Model), 3), (x(Min2Model), 2.2)) → J
  75. Sequence(Text[i, (-7.9, i + 3 - 0.1)], i, -5, 2) → listyySkewLeft
  76. FractionText(1 / (n + 1)) → fraction1
  77. FractionText(1 / (n + 1)) → fraction2
  78. Textfield(μ) → μInput
  79. Textfield(σ) → σInput
  80. Textfield(λ) → λInput
  81. Textfield(β) → βInput
  82. Textfield(s) → sInput
  83. Textfield(μ_M) → μ_mInput
  84. Textfield(σ_M) → σ_MInput
  85. Textfield(λ_M) → λ_mInput
  86. Textfield(β_M) → β_mInput
  87. Textfield(s_M) → s_mInput
  88. Polygon((x(Corner[2]) - 5.5, y(Corner[2])), Corner[2], Corner[3] + 1, (x(Corner[3]) - 5.5, y(Corner[3]) + 1)) → sidebar2, j, q, r, t
  89. Textfield(n) → nInput

AI 绘图提示语参考

绘制QQ图（Quantile-Quantile Plot），用于比较两个数据集的分布。第一个数据集由随机数生成，服从正态、伽马或指数分布等；第二个数据集是这些分布的理论累积分布函数。QQ图将数据点与理论曲线对应，展示数据分布与理论分布的相似性。构造时，先生成随机样本，计算每个分位数对应的累积概率，然后绘制数据分位数与理论分位数曲线的对比图。
以上提示语为根据原始绘图命令整理而来，仅供参考。