 Review of median stable distributions and Schröder’s equationGib Bassett Journal of Econometrics, 2019, vol. 213, issue 1, 289-295 Abstract: Median stable distributions are an extension of traditional (mean) stable distributions. The traditional definition of stability (in terms of sums of iid random variables) is recast as a condition on the sampling distribution of an estimator. For the traditional (mean) stable distribution, the sample mean’s (rescaled) sampling distribution is identical to the distribution of the iid data. Median stable distributions are defined similarly by replacing the sample mean with the sample median. Since the sampling distribution of the median is a functional its stable distribution is the solution to a functional equation. It turns out that this defining functional equation is an instance of a famous equation due to Schröder from 1870. The fame of the equation is due to the way it incorporates iteration of functions, a key feature of what many years later would become dynamic systems analysis. The current paper reviews median stable distributions in light of its connection to Schröder’s functional equation. Keywords: Median stable distributions; Schröder’s functional equation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:213:y:2019:i:1:p:289-295 DOI: 10.1016/j.jeconom.2019.04.016 Access Statistics for this article Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson More articles in Journal of Econometrics from Elsevier |
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