Classify distributions
Classify distributions using the AJUS-system introduced by Galtung (1969).
ajus(V, tolerance=0.1, variant="modified")
V |
A frequency vector |
tolerance |
Specify how similar values have to be to be treated as different (optional). Differences smaller than or equal to the tolerance are ignored. |
variant |
Strict AJUS following Galtung, or modified to include F and L types (default) |
This function implements the AJUS-system introduced by Galtung (1969). The input is a frequency vector; the output is a classification of the distribution.
Distributions are classified as A if they are unimodal with a peak in the centre, as J if they are unimodal with a peak at either end, as U if they are bimodal with a peak at both ends, and as S if they are multimodal. In addition to Galtung's classification, the function classifies distributions as F if there is no peak and all values are more or less the same (flat). Furthermore, a distinction is drawn between J and L distributions, depending on whether they increase or decrease: J types have a peak on the right, L types have the peak on the left. The skew is given as +1 for a positive skew, as 0 for no skew, and -1 for a negative skew.
The skew is identified by comparing the sum of values left and right of the midpoint respectively. For J-type of distributions, the skew is identified on the basis of the changes between values. This way, long tails cannot influence the skew, and a single peak at the left and right-hand end can be differentiated in all cases.
The aim of the AJUS system is to reduce complexity. Initially the intuition was to classify distributions on an ad-hoc basis (i.e. eye-balling). Using an algorithm is certainly more reliable, and useful if one is interested in classifying (and comparing) a large number of distributions. The argument tolerance, however is not a trivial choice and can affect results. Use the helper function ajusCheck to check sensitivity to different values of the tolerance parameter.
You can choose between a strict AJUS classification and a modified AJUSFL classification (default). The AJUS classification does not include a type for distributions without peaks (F type), and NA is returned instead. The AJUS classification does not draw a distinction between unimodal distributions with a peak at the end: the skew needs to be considered to distinguish between increasing and decreasing cases. The modified variant (default) includes the F type and the L type along with the original AJUS types.
The function returns a list. The type returns a string corresponding to the pattern described by Galtung (A,J,U,S) or (F,L). The skew returns a number to describe the direction of the skew. The pattern returns the simplified pattern of the distribution. It indicates whether two values were considered the same (0), or if there was an increase (1) or decrease (-1) between two consecutive values. The length of the pattern is equal to the length of the frequency vector minus one.
Didier Ruedin
Galtung, J. (1969) Theory and Methods of Social Research. Oslo: Universitetsforlaget.
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