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http://dx.doi.org/10.7465/jkdi.2017.28.1.87

Multivariate empirical distribution functions and descriptive methods  

Hong, Chong Sun (Department of Statistics, Sungkyunkwan University)
Park, Jun (Department of Statistics, Sungkyunkwan University)
Park, Yong Ho (Department of Statistics, Sungkyunkwan University)
Publication Information
Journal of the Korean Data and Information Science Society / v.28, no.1, 2017 , pp. 87-98 More about this Journal
Abstract
The multivaiate empirical distribution function (MEDF) is defined in this work. The MEDF's expectation and variance are derived and we have shown the MEDF converges to its real distribution function. Based on random samples from bivariate standard normal distribution with various correlation coefficients, we also obtain MEDFs and propose two kinds of graphical methods to visualize MEDFs on two dimensional plane. One is represented with at most n stairs with similar arguments as the step function, and the other is described with at most n curves which look like bivariate quantile vector. Even though these two descriptive methods could be expressed with three dimensional space, two dimensional representation is obtained with ease and it is enough to explain characteristics of bivariate distribution functions. Hence, it is possible to visualize trivariate empirical distribution functions with three dimensional quantile vectors. With bivariate and four variate illustrative examples, the proposed MEDFs descriptive plots are obtained and explored.
Keywords
Convergence; correlation; empirical distribution; order statistic; quantile vector;
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Times Cited By KSCI : 5  (Citation Analysis)
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