A method is presented for constructing a quadratic spline function satisfying area-matching conditions and local monotonicity constraints, according to the frequencies on the class intervals and to the shape of a given histogram. Such a function is “as close as possible” to the quadratic spline that satisfies the area-matching conditions and the minimum curvature property and generally exhibits a visually pleasing graph.
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Morandi et al. (1989) studied this question.
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