Taylor's law and heavy-tailed distributions

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Abstract

Lionel Roy Taylor’s law of the mean (TLM), also known as Taylor’s law (1⇓–3), can be described succinctly as<br><br>sample variance ∼a (sample mean)^b, a>0, b>0,<br><br>for a sample of positive elements. Careful consideration of TLM raises two unanswered fundamental questions in natural and statistical science.<br>1) Is TLM a unique phenomenon in nature, or should alternative extensions and refinements of TLM, exploiting higher moments and various measures for dependence (association), be explored?<br>2) What are the proper measures for the location, spread, asymmetry, and dependence (association) for random samples with infinite mean?<br><br>In this commentary, we explore both of these fundamental questions.
Original languageEnglish
JournalProceedings of the National Academy of Sciences, USA
DOIs
StatePublished - Dec 14 2021

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