# A note on the coefficients of elliptical random variables

*Tomer Shushi*

*Statistics & Probability Letters*, 2019, vol. 152, issue C, 153-155

**Abstract:**
It is well-known that the sum of elliptical random variables with constant coefficients is also an elliptical random variable. In this note, we prove that the coefficients can also be random variables, such that the sum of elliptical random variables with random coefficients on a circle is also elliptically distributed. We then examine statistical implications by considering the projection pursuit with the underlying random variables.

**Keywords:** Elliptical distributions; Projection pursuit; Stopping rules; Weighted-sum; Wiener process (search for similar items in EconPapers)

**Date:** 2019

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