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Summary measures of probability distributions
Statistical summary measures aim to comprise relevant information from the distribution of a variable of interest. Despite their attractive simplicity, central tendency measures are not always appropriate when we intend to describe the entire distribution. The sample mean, for example, provides practical but often insufficient information. Conversely, a set of sample quantiles can provide a more detailed picture but lack information on how the distribution behaves between elements of the set. We propose to summarize the variable’s distribution by specifying a grid of proportions that divide its mean into a sum of components. From these components, one can easily derive the variable’s expected value on different segments of its support. Our approach results in a setvalued summary measure, which we refer to as compound expectation, that describes the variable’s entire distribution in terms of expected values, and whose elements relate to specific fractions of the variable’s support. 

Papers
GarcíaPareja C, Bottai M. On mean decomposition for summarizing conditional distributions. Stat, 2018, 7:e208 
Presentations
July 16–18, 2018 Mean survival time by ordered fractions of population with censored data Poster (awarded second best poster presentation) Conference proceedings paper 33rd International Workshop on Statistical Modelling, Bristol, UK September 4, 2015 Estimating compound expectation in a regression framework with the new cereg command 2015 Nordic and Baltic Stata Users Group Meeting, Stockholm, Sweden 
Unit of Biostatistics, Nobels väg 13, Karolinska Institutet, 17177 Stockholm, Sweden 