The Quantile Methods to Analyze Distributional Data

This chapter presents the quantile approach for the analysis of distributional data. This consists in representing each distributional observation by a given set of quantiles, thereby transforming the distributional data array to a standard numerical data array. The number m of quantiles used controls the granularity, therefore, a set of m+1 numerical vectors, called the quantile vectors, represents each object. The methods developed then explore the monotonicity property of quantile vectors. Visualization of each object is made by parallel monotone line graphs. Principal Component Analysis is applied to the quantile vectors based on the rank order correlation coefficients. Hierarchical conceptual clustering is performed based on the quantile vectors and on the concept sizes of the p-dimensional hyper-rectangles spanned by the quantile vectors. An application illustrates the proposed approaches.