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Descriptions and Quantifications of Univariate Samples: Numerical Summaries
Published in P. A. W. Lewis, E. J. Orav, Simulation Methodology for Statisticians, Operations Analysts, and Engineers, 2017
The center of a symmetric, unimodal distribution can be estimated by the sample average, which is discussed below, by the sample median, to be considered in Section 6.3, or by more recently introduced robust measures such as the trimean, trimmed mean, or biweight mean (Hoaglin, Mosteller, and Tukey, 1983; see also the histogram program HISTPC in the software supplement to this book). Choosing the “best” estimator among these is a complicated problem that depends on the unknown distribution of the data and cannot be dealt with in this overview. An example in Section 8.2 does illustrate how long-tailed distributions require robust estimators like the median, and further reading should be done in Hoaglin, Mosteller, and Tukey (1983).
TriBeC: identifying influential users on social networks with upstream and downstream network centrality
Published in International Journal of General Systems, 2023
Formally, TriBeC (TB or ) centrality of any node in undirected (G) and directed network () is defined as in Equations (1) and (2): This is equivalent to the average of betweenness score B(i) as well as upstream USB(i) and downstream DSB(i) betweenness centrality, respectively. The weights are taken in analogous to trimean metric formulation which is defined as the average of the median and the midhinge. In our case, midhinge refers to the average of upstream USB(i) and downstream DSB(i) betweenness centrality respectively, whereas median is betweenness B(i) centrality. Further, the foundation of the TriBeC measure operates in three phases, in which the value of USB(i) and DSB(i) are dependent upon B(i). Therefore, the score of upstream and downstream are relative to the most centered node obtained using betweenness centrality. The node which is having a maximum betweenness centrality score will act as a median in a network. The following section depicts the step-wise computations along with the definitions.
Artificial Color Constancy via GoogLeNet with Angular Loss Function
Published in Applied Artificial Intelligence, 2020
Tables 1 and 2 present the comparison of our results with current state-of-the-art algorithms. Several standard metrics are reported in terms of angular error in degrees: mean, median, trimean or standard deviation, mean of the lowest 25% of errors, mean of the highest 25% of errors, and 95th percentile. For reasons unknown, very limited statistical data were reported in the case of Grayball dataset; however, there is no such problem in the case of ColorChecker dataset.