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Cluster Analysis for Applications by Michael R. Anderberg (Auth.)

By Michael R. Anderberg (Auth.)

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Example text

Now divide the interval [a,b] into n equal segments, each of length L = (b- a)/n. The separation points between segments are then yi=yt-i+L, yn = b. ,/I- 1, The proportional of the population falling in the /th segment from yt_x to yt These results can then be used to construct a model of the following form : The observed data are from an underlying distribution of known form. The classes in the data are defined by dividing the abscissa into n equal length segments. , FO,) - F O ^ ) . 0210 Fig.

11. 0, «B = 5, xc = 73 A, nc = 9. 1. Assuming equal expected costs of misclassification, Eq. 0. 7,95). 0 is suppressed since the B class effectively separates the A and C classes. Now suppose the costs of misclassification are all equal and the proportions for the populations are estimated using Eq. 5). Then Eq. 5. The elimination of one group may be either acceptable or objectionable depending on the particular purpose of the study and the role the categorized variable is to play. The reference variable in the example might be taken to have its classes ordered as C > B > A.

The classes in the data are defined by dividing the abscissa into n equal length segments. , FO,) - F O ^ ) . 0210 Fig. 3. Distribution among normal classes for various choices of truncation points. 3. 4. In both of these cases the distribution has a finite domain which is taken to range from the smallest to the largest of the actual observations. Distributions with infinite domains such as the gamma and normal result in some complications. To obtain correspondence with the finite range of values in the sample it is necessary to truncate the distribution.