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Additional info for Grade Models and Methods for Data Analysis: With Applications for the Analysis of Data Populations
The same applies for cdf's of random variables which are not Lilliputian. 3. 2 (continuous Lilliputian variable). A Lilliputian variable will be called continuous if its cdf is continuous and its derivative fdu) = dFdu)/du, called the density of ~, exists almost everywhere relative to Lebesgue measure. Illustration (three continuous Lilliputian variables): In Fig. 8, < u < 1. 8 Note that the graphs of FI and F2 in Fig. 1 are continuous with no horizontal segments, and that the graph of F3 contains a horizontal segment.
00 • First we normalize the data by dividing each amount by its distribution total (200 for country A, and 300 for country B). Normalizing puts all data values on a 0 to 1 scale. Note: The word "normalize" often has different meanings in other statistical fields . • Next is the grade transformation. ) To obtain the grade transformed values, the normalized values are accumulated (here, from left to right) across the categories. Note: The concept of the grade transformation will be extended in the theory sections of Chapter 3.
1 is plotted on a coordinate system called the unit square. Each axis displays the cumulative proportions, and covers the range of 0 to 1. Note: In addition to the five line segments, each representing one of the five categories, a line referred to as the diagonal (or "identical" distribution line) has been added to the figure. 2. 1. The concentration curve plotted on the unit square. Distribution of spending for country A relative to country B. ) Note: The diagonal represents the concentration "curve" that would exist if the proportions for both country A and country B were the same within each category.