TY - JOUR
T1 - Taylor's law and heavy-tailed distributions
AU - Lindquist, William
AU - Rachev, Svetlozar
PY - 2021/12/14
Y1 - 2021/12/14
N2 - Lionel Roy Taylor’s law of the mean (TLM), also known as Taylor’s law (1⇓–3), can be described succinctly assample variance ∼a (sample mean)^b, a>0, b>0,for a sample of positive elements. Careful consideration of TLM raises two unanswered fundamental questions in natural and statistical science.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?2) What are the proper measures for the location, spread, asymmetry, and dependence (association) for random samples with infinite mean?In this commentary, we explore both of these fundamental questions.
AB - Lionel Roy Taylor’s law of the mean (TLM), also known as Taylor’s law (1⇓–3), can be described succinctly assample variance ∼a (sample mean)^b, a>0, b>0,for a sample of positive elements. Careful consideration of TLM raises two unanswered fundamental questions in natural and statistical science.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?2) What are the proper measures for the location, spread, asymmetry, and dependence (association) for random samples with infinite mean?In this commentary, we explore both of these fundamental questions.
U2 - 10.1073/pnas.2118893118
DO - 10.1073/pnas.2118893118
M3 - Article
JO - Proceedings of the National Academy of Sciences, USA
JF - Proceedings of the National Academy of Sciences, USA
ER -