Grade Models and Methods for Data Analysis

dependence function and the Gini Index.- 7.7 Appendix - Bibliographical remarks.- 8 Dependence Lilliputian Model.- 8.1 Introduction.- 8.2 Grade bivariate distributions and overrepresentation maps for probability tables.- 8.4 Spearman's rho and Kendall's tau expressed by volumes and masses in the unit cube.- 8.5 Grade regression functions and related measures.- 8.6 On permuting rows and columns of m × k probability tables.- 8.7 The hinged sequences of rows and columns.- 8.8 Appendix: Bibliographical remarks.- 9 Grade Correspondence Analysis and outlier detection.- 9.1 Introduction.- 9.2 Algorithms of GCA.- 9.3 Algorithm for Smooth Grade Correspondence Analysis (SGCA).- 9.4 Examples of GCA and SGCA results.- 9.5 Detection of rows and columns outlying the main trend.- 9.6 Appendix - Bibliographical remarks.- 10 Cluster analysis based on GCA.- 10.1 Introduction.- 10.2 Single and double grade clustering.- 10.3 Optimal grade clustering.- 10.4 Cluster analysis in the detection of mixtures.- 10.5 Cluster analysis and the detection of an imprecisely defined trend.- 10.6 On GCCA application to various data sets.- 10.7 Appendix.- 11 Regularity and the number of clusters.- 11.1 Introduction.- 11.2 Generalization of the parabola family from the .- 11.3 The ideal regularity of two-way data tables.- 11.4 Regularity and cluster detection.- 11.5 Cluster detection in finite data tables.- 11.6 Appendix - Bibliographical remarks.- 12 Grade approach to the analysis of finite data matrices.- 12.1 Introduction.- 12.2 Insight Examples.- 12.3Applicability of GCA.- 12.4 A revisit of the univariate data.- 12.5 Finite multivariate datasets and related inequality measures.- 12.6 Transformations of variables.- 12.7 Detection of outliers and decomposition of a dataset.- 13 Inequality measures for multivariate distributions.- 13.1 Introduction.- 13.2 Inequality measures for multivariate distributions with finite sets of records.- 13.3 Inequality measures for multivariate distributions with nonfinite sets of records.- 13.4 Inequality measures for continuous bivariate distributions.- 13.5 Inequality measures for grade multinormal distributions.- 13.6 Inequality measures for the Moran distributions.- 13.7 Appendix - link between grade similarity and dissimilarity of two regularly dependent random variables.- 14 Case studies with multivariate data.- 14.1 Introduction.- 14.2 Case Study 1 - Main Trend of Questionnaire Data.- 14.3 Case Study 1 - Decomposition of the dataset into regular subpopulations.- 14.4 Case Study 2 - Analysis of Engineering Data (Strength of Concrete).- 14.5 Case Study 2 - Decomposition of concrete mixtures into FITMT and OUT-MT.- 14.6 Final remarks for the two case studies.- 14.7 Appendix.- 15 The GradeStat program.- 15.1 Introduction.- 15.2 Main implemented features.- References.