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May 28th, 2015
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  1. Tukey = Function[x,
  2. l = Length[x];
  3. xx = Sort[x];
  4. xx[[Ceiling[l/2]]] +
  5. 0.185*(xx[[Ceiling[0.95*l]]] +
  6. xx[[Ceiling[0.05*l]]] -
  7. 2*xx[[Ceiling[0.5*l]]])
  8. ];
  9.  
  10. n = 50;
  11. p1 = 0;
  12. p2 = 1;
  13. eeps = 5;
  14. eps = 0.1;
  15.  
  16. dov = 5; (* Доверительная вероятность в процентах *)
  17. dov = dov/2;
  18.  
  19. v1 = List[];
  20. v1 = Join[RandomVariate[NormalDistribution[p1, p2], n]];
  21.  
  22. v2 = List[];
  23. v2 = Join[v2, RandomVariate[NormalDistribution[p1, p2], n - n*eps]];
  24. v2 = Join[v2, RandomVariate[NormalDistribution[p1 + eeps, p2], n*eps]];
  25. v2 = RandomSample[v2];
  26.  
  27. v3 = List[];
  28. v3 = Join[v3, RandomVariate[NormalDistribution[p1, p2], n - n*eps]];
  29. v3 = Join[v3, RandomVariate[NormalDistribution[p1, p2 + eeps], n*eps]];
  30. v3 = RandomSample[v3];
  31.  
  32. bv11 = List[];
  33. bv12 = List[];
  34. bv21 = List[];
  35. bv22 = List[];
  36. bv31 = List[];
  37. bv32 = List[];
  38.  
  39. For[i = 1, i <= n, i++,
  40. bv11 = Append[bv11, Tukey[RandomChoice[v1, Length[v1]]]];
  41. bv12 = Append[bv12, Median[RandomChoice[v1, Length[v1]]]];
  42.  
  43. bv21 = Append[bv21, Tukey[RandomChoice[v2, Length[v2]]]];
  44. bv22 = Append[bv22, Median[RandomChoice[v2, Length[v2]]]];
  45.  
  46. bv31 = Append[bv31, Tukey[RandomChoice[v3, Length[v3]]]];
  47. bv32 = Append[bv32, Median[RandomChoice[v3, Length[v3]]]];
  48. ]
  49.  
  50. text = "";
  51.  
  52. Print["Оценка Тьюки - ", Mean[bv11], " - ", Variance[bv11],
  53. " - {", Sort[bv11][[Ceiling[(0 + (dov/100))*Length[bv11]]]], "; ",
  54. Sort[bv11][[Ceiling[(1 - (dov/100))*Length[bv11]]]], "}"];
  55. Print["Выборочная медиана - ", Mean[bv12], " - ", Variance[bv12],
  56. " - {", Sort[bv12][[Ceiling[(0 + (dov/100))*Length[bv12]]]], "; ",
  57. Sort[bv12][[Ceiling[(1 - (dov/100))*Length[bv12]]]], "}"];
  58. Print[];
  59. Print["Оценка Тьюки(ассиметричный выброс) - ", Mean[bv21], " - ",
  60. Variance[bv21],
  61. " - {", Sort[bv21][[Ceiling[(0 + (dov/100))*Length[bv21]]]], "; ",
  62. Sort[bv21][[Ceiling[(1 - (dov/100))*Length[bv21]]]], "}"];
  63. Print["Выборочная медиана(ассиметричный выброс) - ", Mean[bv22],
  64. " - ", Variance[bv22],
  65. " - {", Sort[bv22][[Ceiling[(0 + (dov/100))*Length[bv22]]]], "; ",
  66. Sort[bv22][[Ceiling[(1 - (dov/100))*Length[bv22]]]], "}"];
  67. Print[]
  68. Print["Оценка Тьюки(симметричный выброс) - ", Mean[bv31], " - ",
  69. Variance[bv31],
  70. " - {", Sort[bv31][[Ceiling[(0 + (dov/100))*Length[bv31]]]], "; ",
  71. Sort[bv31][[Ceiling[(1 - (dov/100))*Length[bv31]]]], "}"];
  72. Print["Выборочная медиана(симметричный выброс) - ", Mean[bv32], " - ",
  73. Variance[bv32],
  74. " - {", Sort[bv32][[Ceiling[(0 + (dov/100))*Length[bv32]]]], "; ",
  75. Sort[bv32][[Ceiling[(1 - (dov/100))*Length[bv32]]]], "}"];
  76.  
  77. \[ScriptCapitalD] = SmoothKernelDistribution[v1];
  78. Print[Table[
  79. Plot[f[\[ScriptCapitalD], x], {x, p1 - 8, p1 + 8},
  80. PlotLabel -> f], {f, {PDF, CDF}}]];
  81. \[ScriptCapitalD] = SmoothKernelDistribution[v2];
  82. Print[Table[
  83. Plot[f[\[ScriptCapitalD], x], {x, p1 - 8, p1 + 8},
  84. PlotLabel -> f], {f, {PDF, CDF}}]];
  85. \[ScriptCapitalD] = SmoothKernelDistribution[v3];
  86. Print[Table[
  87. Plot[f[\[ScriptCapitalD], x], {x, p1 - 8, p1 + 8},
  88. PlotLabel -> f], {f, {PDF, CDF}}]];
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