Order statistics are a subset of the field of statistics which deal with the arrangement, or ordering, of data points. Order statistics are used to describe the distribution of a population of data points, in terms of their ranks, or order, within the data set. Specifically, order statistics are used to determine the median, mode, quartiles, and other measures of central tendency and dispersion.
Order statistics are useful in many different fields, including medicine, economics, and engineering. In medicine, order statistics are used to measure the effectiveness of treatments and to compare the performance of different treatments. In economics, order statistics are used to measure the health of an economy and to compare the performance of different economic indicators. In engineering, order statistics are used to analyze the performance of complex systems.
Order statistics are typically divided into two categories: univariate and multivariate. Univariate order statistics are used to describe the distribution of a single variable, such as the median or mode of a data set. Multivariate order statistics are used to describe the distributions of multiple variables, such as the interquartile range or standard deviation of a data set.
There are a variety of methods for computing order statistics. These include the traditional method of ranking data points from smallest to largest, as well as more modern methods such as the fast Fourier transform and the use of sorting algorithms. In addition, many software packages are available which can be used to compute order statistics.
Order statistics provide an invaluable tool for understanding and interpreting data sets. By providing measures of central tendency and dispersion, they can be used to identify trends and outliers, and to compare the performance of different treatments, economic indicators, or systems.
References
Chen, S., & Duan, Y. (2015). Order Statistics. In Encyclopedia of Social Measurement (pp. 574-576). Academic Press.
Dixon, W. J., & Massey, F. J. (1977). Introduction to Statistical Analysis. New York, NY: McGraw-Hill.
Harter, S. L. (2011). Order Statistics: Applications in Reliability and Quality Control. John Wiley & Sons.
Kendall, M. G., & Stuart, A. (1979). The Advanced Theory of Statistics. London, UK: Charles Griffin & Company.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (2007). Numerical Recipes: The Art of Scientific Computing. Cambridge, UK: Cambridge University Press.