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In social science research, differences among groups or changes over time are a common focus of study. While means and variances are typically the basis for statistical methods used in this research, the underlying social theory often implies properties of distributions that are not well captured by these summary measures. Examples include the current controversies regarding growing inequality in earnings, racial differences in test scores, socio-economic correlates of birth outcomes, and the impact of smoking on survival and health. The distributional differences that animate the debates in these fields are complex. They comprise the usual mean-shifts and changes in variance, but also more subtle comparisons of changes in the upper and lower tails of distributions. Survey and census data on such attributes contain a wealth of distributional information, but traditional methods of data analysis leave much of this information untapped. In this monograph, we present methods for full comparative distributional analysis. The methods are based on the relative distribution, a nonparametric complete summary of the information required for scale--invariant comparisons between two distributions. The relative distribution provides a general integrated framework for analysis. It offers a graphical component that simplifies exploratory data analysis and display, a statistically valid basis for the development of hypothesis-driven summary measures, and the potential for decomposition that enables one to examine complex hypotheses regarding the origins of distributional changes within and between groups. The monograph is written for data analysts and those interested in measurement, and it can serve as a textbook for a course on distributional methods. The presentation is application oriented,.

Social sciences --- Distribution (Probability theory) --- Statistical methods. --- Quantitative methods in social research --- Mathematical statistics --- Statistics. --- Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law. --- Statistics for Social Science, Behavioral Science, Education, Public Policy, and Law. --- Statistics for Social Sciences, Humanities, Law. --- Statistics . --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities

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Complex analysis --- Artificial intelligence. Robotics. Simulation. Graphics --- Algorithms --- Machine Learning --- Machine learning --- Kernel functions --- Engineering & Applied Sciences --- Computer Science --- Algorithms. --- Kernel functions. --- Machine learning. --- 519.213 --- #TELE:SISTA --- 681.3*I26 --- Learning, Machine --- Functions, Kernel --- Algorism --- 519.213 Probability distributions and densities. Normal distribution. Characteristic functions. Measures of dependence. Infinitely divisible laws. Stable laws --- Probability distributions and densities. Normal distribution. Characteristic functions. Measures of dependence. Infinitely divisible laws. Stable laws --- 681.3*I26 Learning: analogies; concept learning; induction; knowledge acquisition; language acquisition; parameter learning (Artificial intelligence)--See also {681.3*K32} --- Learning: analogies; concept learning; induction; knowledge acquisition; language acquisition; parameter learning (Artificial intelligence)--See also {681.3*K32} --- Artificial intelligence --- Machine theory --- Functions of complex variables --- Geometric function theory --- Algebra --- Arithmetic --- Foundations --- E-books

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