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Variability Orders

In: Stochastic Comparisons with Applications

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  • Subhash C. Kochar

    (Portland State University, Fariborz Maseeh Department of Mathematics and Statistics)

Abstract

Most of the classical methods for comparing variability among distributions are based only upon summary statistics such as variance and standard deviation, which are very crude though convenient methods to use. It is possible that one variable is more spread out than the second initially, but later on it is the other way around. Variance and other summary statistics cannot detect such differences. Like stochastic orders for comparing magnitudes of random variables, several stochastic orders for comparing variabilities of random variables based on more detailed examinations of their entire distribution functions have been proposed and studied in the literature. These include the dispersive, the right spread (also known by excess wealth), peakedness, and convex orders. These stochastic orders and their properties are explained with the help of several examples. Some non-parametric tests for variability are also discussed briefly.

Suggested Citation

  • Subhash C. Kochar, 2022. "Variability Orders," Springer Books, in: Stochastic Comparisons with Applications, chapter 0, pages 63-89, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-12104-3_3
    DOI: 10.1007/978-3-031-12104-3_3
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