Introduction to descriptive (Maxima Manual)

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### 39.1 Introduction to descriptive

Package `descriptive` contains a set of functions for making descriptive statistical computations and graphing. Together with the source code there are three data sets in your Maxima tree: `pidigits.data`, `wind.data` and `biomed.data`.

Any statistics manual can be used as a reference to the functions in package `descriptive`.

For comments, bugs or suggestions, please contact me at ’mario AT edu DOT xunta DOT es’.

Here is a simple example on how the descriptive functions in `descriptive` do they work, depending on the nature of their arguments, lists or matrices,

    (%i1) load ("descriptive")$

    (%i2) /* univariate sample */   mean ([a, b, c]);
                                c + b + a
    (%o2)                       ---------
                                    3

    (%i3) matrix ([a, b], [c, d], [e, f]);
                                [ a  b ]
                                [      ]
    (%o3)                       [ c  d ]
                                [      ]
                                [ e  f ]

    (%i4) /* multivariate sample */ mean (%);
                          e + c + a  f + d + b
    (%o4)                [---------, ---------]
                              3          3

Note that in multivariate samples the mean is calculated for each column.

In case of several samples with possible different sizes, the Maxima function `map` can be used to get the desired results for each sample,

    (%i1) load ("descriptive")$

    (%i2) map (mean, [[a, b, c], [d, e]]);
                            c + b + a  e + d
    (%o2)                  [---------, -----]
                                3        2

In this case, two samples of sizes 3 and 2 were stored into a list.

Univariate samples must be stored in lists like

    (%i1) s1 : [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5];
    (%o1)           [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5]

and multivariate samples in matrices as in

    (%i1) s2 : matrix ([13.17, 9.29], [14.71, 16.88], [18.50, 16.88],
                 [10.58, 6.63], [13.33, 13.25], [13.21,  8.12]);
                            [ 13.17  9.29  ]
                            [              ]
                            [ 14.71  16.88 ]
                            [              ]
                            [ 18.5   16.88 ]
    (%o1)                   [              ]
                            [ 10.58  6.63  ]
                            [              ]
                            [ 13.33  13.25 ]
                            [              ]
                            [ 13.21  8.12  ]

In this case, the number of columns equals the random variable dimension and the number of rows is the sample size.

Data can be introduced by hand, but big samples are usually stored in plain text files. For example, file `pidigits.data` contains the first 100 digits of number `%pi`:

          3
          1
          4
          1
          5
          9
          2
          6
          5
          3 ...

In order to load these digits in Maxima,

    (%i1) s1 : read_list (file_search ("pidigits.data"))$

    (%i2) length (s1);
    (%o2)                          100

On the other hand, file `wind.data` contains daily average wind speeds at 5 meteorological stations in the Republic of Ireland (This is part of a data set taken at 12 meteorological stations. The original file is freely downloadable from the StatLib Data Repository and its analysis is discused in Haslett, J., Raftery, A. E. (1989) Space-time Modelling with Long-memory Dependence: Assessing Ireland’s Wind Power Resource, with Discussion. Applied Statistics 38, 1-50). This loads the data:

    (%i1) s2 : read_matrix (file_search ("wind.data"))$

    (%i2) length (s2);
    (%o2)                          100

    (%i3) s2 [%]; /* last record */
    (%o3)            [3.58, 6.0, 4.58, 7.62, 11.25]

Some samples contain non numeric data. As an example, file `biomed.data` (which is part of another bigger one downloaded from the StatLib Data Repository) contains four blood measures taken from two groups of patients, `A` and `B`, of different ages,

    (%i1) s3 : read_matrix (file_search ("biomed.data"))$

    (%i2) length (s3);
    (%o2)                          100

    (%i3) s3 [1]; /* first record */
    (%o3)            [A, 30, 167.0, 89.0, 25.6, 364]

The first individual belongs to group `A`, is 30 years old and his/her blood measures were 167.0, 89.0, 25.6 and 364.

One must take care when working with categorical data. In the next example, symbol `a` is asigned a value in some previous moment and then a sample with categorical value `a` is taken,

    (%i1) a : 1$

    (%i2) matrix ([a, 3], [b, 5]);
                                [ 1  3 ]
    (%o2)                       [      ]
                                [ b  5 ]

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