有人知道matlab的Anderson-Darling检验（A-D检验）程序吗？

qinyu

如题：A-D检验方法我知道，但是自己编程的话有点复杂。
应该有matlab的AndersoA-D检验）函数吧？

sogooda

1. function [AnDartest] = AnDartest(x,alpha)
   
2. %ANDARTEST Anderson-Darling test for assessing normality of a sample data.
   
3. % The Anderson-Darling test (Anderson and Darling, 1952) is used to test if
   
4. % a sample of data comes from a specific distribution. It is a modification
   
5. % of the Kolmogorov-Smirnov (K-S) test and gives more weight to the tails
   
6. % than the K-S test. The K-S test is distribution free in the sense that the
   
7. % critical values do not depend on the specific distribution being tested.
   
8. % The Anderson-Darling test makes use of the specific distribution in calculating
   
9. % critical values. This has the advantage of allowing a more sensitive test
   
10. % and the disadvantage that critical values must be calculated for each
    
11. % distribution.
    
12. % The Anderson-Darling test is only available for a few specific distributions.
    
13. % The test is calculated as:
    
14. %              
    
15. %        AD2 = integral{[F_o(x)-F_t(x)]^2/[F_t(x)(1-F_t(x)0]}dF_t(x)
    
16. %
    
17. %        AD2a = AD2*a
    
18. %
    
19. % Note that for a given distribution, the Anderson-Darling statistic may be
    
20. % multiplied by a constant, a (which usually depends on the sample size, n).
    
21. % These constants are given in the various papers by Stephens (1974, 1977a,
    
22. % 1977b, 1979, 1986). This is what should be compared against the critical
    
23. % values. Also, be aware that different constants (and therefore critical
    
24. % values) have been published. You just need to be aware of what constant
    
25. % was used for a given set of critical values (the needed constant is typically
    
26. % given with the critical values).
    
27. % The critical values for the Anderson-Darling test are dependent on the
    
28. % specific distribution that is being tested. Tabulated values and formulas
    
29. % have been published for a few specific distributions (normal, lognormal,
    
30. % exponential, Weibull, logistic, extreme value type 1). The test is a one-sided
    
31. % test and the hypothesis that the distribution is of a specific form is
    
32. % rejected if the test statistic, AD2a, is greater than the critical value.
    
33. % Here we develop the m-file for detecting departure from normality. It is
    
34. % one of the most powerful statistics for test this.
    
35. %
    
36. % Syntax: function AnDartest(X)
    
37. %      
    
38. %     Input:
    
39. %          x - data vector
    
40. %      alpha - significance level (default = 0.05)
    
41. %
    
42. %     Output:
    
43. %            - Complete Anderson-Darling normality test
    
44. %
    
45. % Example: From the Table 1 base data of secondary coating diameter, SCD
    
46. %    (micrometers) for an optical fiber manufacturing and testing [Application
    
47. %    and acceptance sampling in testing of optical fiber (Bhaumik and Bhargava,
    
48. %    2005)], taked from Internet:
    
49. %    http://www.sterliteoptical.com/pdf/ProdWithContents/Application%20of%
    
50. %    20acceptance%20sampling%20in%20testing%20of%20optical%20fiber.pdf
    
51. %    The measurements of the sample are analyzed for the normality using the
    
52. %    Anderson-Darling test with a significance of 0.05.
    
53. %   
    
54. % Data vector is:
    
55. %  x=[245.3;245.6;245.0;244.7;244.6;244.6;245.9;245.2;245.5;246.1;246.5;246.7;
    
56. %  246.0;245.8;245.3;245.3;246.0;245.5;246.7;245.3;245.8;245.8;245.2;245.7;
    
57. %  244.8;246.7;246.5;245.5;246.0;244.8;244.8;244.4;244.8;245.6;245.5;244.0;
    
58. %  245.2;244.8;245.4;246.1;245.9;245.6;245.2];
    
59. %
    
60. % Calling on Matlab the function:
    
61. %            AnDartest(x)
    
62. %
    
63. % Answer is:
    
64. %
    
65. % Sample size: 43
    
66. % Anderson-Darling statistic: 0.2858
    
67. % Anderson-Darling adjusted statistic: 0.2912
    
68. % Probability associated to the Anderson-Darling statistic = 0.6088
    
69. % With a given significance = 0.050
    
70. % The sampled population is normally distributed.
    
71. % Thus, this sample have been drawn from a normal population with a mean & variance = 245.4814    0.4139
    
72. %
    
73. % Created by A. Trujillo-Ortiz, R. Hernandez-Walls, K. Barba-Rojo and
    
74. %             A. Castro-Perez
    
75. %             Facultad de Ciencias Marinas
    
76. %             Universidad Autonoma de Baja California
    
77. %             Apdo. Postal 453
    
78. %             Ensenada, Baja California
    
79. %             Mexico.
    
80. %             atrujo@uabc.mx
    
81. %
    
82. % Copyright. April 20, 2007.
    
83. %
    
84. % To cite this file, this would be an appropriate format:
    
85. % Trujillo-Ortiz, A., R. Hernandez-Walls, K. Barba-Rojo and A. Castro-Perez. (2007).
    
86. %   AnDartest:Anderson-Darling test for assessing normality of a sample data.
    
87. %   A MATLAB file. [WWW document]. URL http://www.mathworks.com/matlabcentral/
    
88. %   fileexchange/loadFile.do?objectId=14807
    
89. %
    
90. % References:
    
91. %  Anderson, T. W. and Darling, D. A. (1952), Asymptotic theory of certain
    
92. %      'goodness-of-fit' criteria based on stochastic processes. Annals of
    
93. %      Mathematical Statistics, 23:193-212.
    
94. %  Stephens, M. A. (1974), EDF Statistics for goodness of fit and some
    
95. %      comparisons. Journal of the American Statistical Association,
    
96. %      69:730-737.
    
97. %  Stephens, M. A. (1976), Asymptotic Results for goodness-of-fit statistics
    
98. %      with unknown parameters. Annals of Statistics, 4:357-369.
    
99. %  Stephens, M. A. (1977a), Goodness of fit for the extreme value distribution.
    
100. %      Biometrika, 64:583-588.
     
101. %  Stephens, M. A. (1977b), Goodness of fit with special reference to tests
     
102. %      for exponentiality. Technical Report No. 262, Department of Statistics,
     
103. %      Stanford University, Stanford, CA.
     
104. %  Stephens, M. A. (1979), Tests of fit for the logistic distribution based
     
105. %      on the empirical distribution function. Biometrika, 66:591-595.
     
106. %  Stephens, M. A. (1986), Tests based on EDF statistics. In: D'Agostino,
     
107. %      R.B. and Stephens, M.A., eds.: Goodness-of-Fit Techniques. Marcel
     
108. %      Dekker, New York.
     
109. %
     
110. 
     
111. switch nargin
     
112.     case{2}
     
113.         if isempty(x) == false && isempty(alpha) == false
     
114.             if (alpha <= 0 || alpha >= 1)
     
115.                 fprintf('Warning: Significance level error; must be 0 < alpha < 1 \n');
     
116.                 return;
     
117.             end
     
118.         end
     
119.     case{1}
     
120.         alpha = 0.05;
     
121.     otherwise
     
122.         error('Requires at least one input argument.');
     
123. end
     
124. 
     
125. n = length(x);
     
126. 
     
127. if n < 7,
     
128.     disp('Sample size must be greater than 7.');
     
129.     return,
     
130. else
     
131.     x = x(:);
     
132.     x = sort(x);
     
133.     fx = normcdf(x,mean(x),std(x));
     
134.     i = 1:n;
     
135.    
     
136.     S = sum((((2*i)-1)/n)*(log(fx)+log(1-fx(n+1-i))));
     
137.     AD2 = -n-S;
     
138.    
     
139.     AD2a = AD2*(1 + 0.75/n + 2.25/n^2); %correction factor for small sample sizes: case normal
     
140.    
     
141.     if (AD2a >= 0.00 && AD2a < 0.200);
     
142.         P = 1 - exp(-13.436 + 101.14*AD2a - 223.73*AD2a^2);
     
143.     elseif (AD2a >= 0.200 && AD2a < 0.340);
     
144.         P = 1 - exp(-8.318 + 42.796*AD2a - 59.938*AD2a^2);
     
145.     elseif (AD2a >= 0.340 && AD2a < 0.600);
     
146.         P = exp(0.9177 - 4.279*AD2a - 1.38*AD2a^2);
     
147.     else (AD2a >= 0.600 && AD2a <= 13);
     
148.         P = exp(1.2937 - 5.709*AD2a + 0.0186*AD2a^2);
     
149.     end
     
150. end
     
151. 
     
152. disp(' ')
     
153. fprintf('Sample size: %i\n', n);
     
154. fprintf('Anderson-Darling statistic: %3.4f\n', AD2);
     
155. fprintf('Anderson-Darling adjusted statistic: %3.4f\n', AD2a);
     
156. fprintf('Probability associated to the Anderson-Darling statistic = %3.4f\n', P);
     
157. fprintf('With a given significance = %3.3f\n', alpha);
     
158. if P >= alpha;
     
159.    disp('The sampled population is normally distributed.');
     
160.    s = [mean(x),var(x)];
     
161.    fprintf('Thus, this sample have been drawn from a normal population with a mean & variance = %6.4f  %8.4f\n',s);
     
162. else
     
163.    disp('The sampled population is not normally distributed.');
     
164. end
     
165. 
     
166. return,

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