Changeset 4589 for trunk/library

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Timestamp:
11/12/08 07:48:56 (2 months ago)
Author:
pmoura
Message:

Added calculation of sample and population kurtosis to the "statistics" library.

Location:
trunk/library
Files:
4 modified

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Unmodified
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Removed

  • trunk/library/population.lgt

    r4588 r4589  
    1010 
    1111    skewness([X| Xs], Skewness) :- 
    12         :arithmetic_mean(Xs, 1, Length, X, Mean), 
    13         X2 is (X - Mean) ** 2, 
    14         X3 is (X - Mean) ** 3, 
    15         :squares_and_cubes(Xs, Mean, X2, Squares, X3, Cubes), 
    16         Skew is (Cubes / Length) / (Squares / Length) ** 1.5, 
    17         Skewness is sqrt(Length*(Length - 1)) * Skew / (Length - 2). 
     12        :arithmetic_mean(Xs, 1, N, X, Mean), 
     13        Square is (X - Mean) ** 2, 
     14        Cube is (X - Mean) ** 3, 
     15        :squares_and_cubes(Xs, Mean, Square, Squares, Cube, Cubes), 
     16        Skew is (Cubes / N) / (Squares / N) ** 1.5, 
     17        Skewness is sqrt(N*(N - 1)) * Skew / (N - 2). 
     18 
     19    kurtosis([X| Xs], Kurtosis) :- 
     20        :arithmetic_mean(Xs, 1, N, X, Mean), 
     21        Square is (X - Mean) ** 2, 
     22        Hyper is (X - Mean) ** 4, 
     23        :squares_and_hypers(Xs, Mean, Square, _, Hyper, Hypers), 
     24        :variance(Xs, 1, N, X, 0, M2), 
     25        K2 is M2 / (N - 1), 
     26        Kurtosis is N*(N + 1)*Hypers / ((N- 1)*(N- 2)*(N -3)*K2**2) - 3*(N -1)**2/((N- 2)*(N -3)). 
    1827 
    1928    standard_deviation([X| Xs], Deviation) :- 
    20         :variance(Xs, 1, Length, X, 0, M2), 
    21         Deviation is sqrt(M2 / Length). 
     29        :variance(Xs, 1, N, X, 0, M2), 
     30        Deviation is sqrt(M2 / N). 
    2231 
    2332    variance([X| Xs], Variance) :- 
    24         :variance(Xs, 1, Length, X, 0, M2), 
    25         Variance is M2 / Length. 
     33        :variance(Xs, 1, N, X, 0, M2), 
     34        Variance is M2 / N. 
    2635 
    2736:- end_object. 

  • trunk/library/sample.lgt

    r4588 r4589  
    1010 
    1111    skewness([X| Xs], Skewness) :- 
    12         :arithmetic_mean(Xs, 1, Length, X, Mean), 
    13         X2 is (X - Mean) ** 2, 
    14         X3 is (X - Mean) ** 3, 
    15         :squares_and_cubes(Xs, Mean, X2, Squares, X3, Cubes), 
    16         Skewness is (Cubes / Length) / (Squares / Length) ** 1.5. 
     12        :arithmetic_mean(Xs, 1, N, X, Mean), 
     13        Square is (X - Mean) ** 2, 
     14        Cube is (X - Mean) ** 3, 
     15        :squares_and_cubes(Xs, Mean, Square, Squares, Cube, Cubes), 
     16        Skewness is (Cubes / N) / (Squares / N) ** 1.5. 
     17 
     18    kurtosis([X| Xs], Kurtosis) :- 
     19        :arithmetic_mean(Xs, 1, N, X, Mean), 
     20        Square is (X - Mean) ** 2, 
     21        Hyper is (X - Mean) ** 4, 
     22        :squares_and_hypers(Xs, Mean, Square, Squares, Hyper, Hypers), 
     23        Kurtosis is (Hypers / N) / (Squares / N) ** 2 - 3. 
    1724 
    1825    standard_deviation([X| Xs], Deviation) :- 
    19         :variance(Xs, 1, Length, X, 0, M2), 
    20         Deviation is sqrt(M2 / (Length - 1)). 
     26        :variance(Xs, 1, N, X, 0, M2), 
     27        Deviation is sqrt(M2 / (N - 1)). 
    2128 
    2229    variance([X| Xs], Variance) :- 
    23         :variance(Xs, 1, Length, X, 0, M2), 
    24         Variance is M2 / (Length - 1). 
     30        :variance(Xs, 1, N, X, 0, M2), 
     31        Variance is M2 / (N - 1). 
    2532 
    2633:- end_object. 

  • trunk/library/statistics.lgt

    r4588 r4589  
    8282        Cacc2 is Cacc + (X - Mean) ** 3, 
    8383        squares_and_cubes(Xs, Mean, Sacc2, Squares, Cacc2, Cubes). 
     84 
     85    squares_and_hypers([], _, Squares, Squares, Hypers, Hypers). 
     86    squares_and_hypers([X| Xs], Mean, Sacc, Squares, Hacc, Hypers) :- 
     87        Sacc2 is Sacc + (X - Mean) ** 2, 
     88        Hacc2 is Hacc + (X - Mean) ** 4, 
     89        squares_and_hypers(Xs, Mean, Sacc2, Squares, Hacc2, Hypers). 
    8490 
    8591    median([X| Xs], Median) :- 

  • trunk/library/statisticsp.lgt

    r4483 r4589  
    102102    :- info(skewness/2, 
    103103        [comment is 'Calculates the skewness of a list of numbers. Fails if the list is empty.', 
    104          argnames is ['List', 'Deviation']]). 
     104         argnames is ['List', 'Skewness']]). 
     105 
     106    :- public(kurtosis/2). 
     107    :- mode(kurtosis(+list(number), -float), zero_or_one). 
     108    :- info(kurtosis/2, 
     109        [comment is 'Calculates the (excess) kurtosis of a list of numbers. Fails if the list is empty.', 
     110         argnames is ['List', 'Kurtosis']]). 
    105111 
    106112    :- public(variance/2). 
    … …  
    116122        argnames is ['Term']]). 
    117123 
    118     :- private(arithmetic_mean/5). 
    119     :- private(squares_and_cubes/6). 
     124    :- private(arithmetic_mean/5). 
     125    :- private(squares_and_cubes/6). 
     126    :- private(squares_and_hypers/6). 
    120127    :- private(variance/6). 
    121128