Barczy, Mátyás and Burai, Pál József (2022) Limit theorems for Bajraktarevic and Cauchy quotient means of independent identically distributed random variables. AEQUATIONES MATHEMATICAE, 96 (2). pp. 279305. ISSN 00019054

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Abstract
We derive strong laws of large numbers and central limit theorems for Bajraktarevic, Gini and exponential (also called Betatype) and logarithmic Cauchy quotient means of independent identically distributed (i.i.d.) random variables. The exponential and logarithmic Cauchy quotient means of a sequence of i.i.d. random variables behave asymptotically normal with the usual square root scaling just like the geometric means of the given random variables. Somewhat surprisingly, the multiplicative Cauchy quotient means of i.i.d. random variables behave asymptotically in a rather different way: in order to get a nontrivial normal limit distribution a time dependent centering is needed.
Item Type:  Article 

Uncontrolled Keywords:  central limit theorem; Delta method; Bajraktarević mean; Gini mean; Cauchy quotient means; Betatype mean; 
Subjects:  Q Science / természettudomány > QA Mathematics / matematika 
SWORD Depositor:  MTMT SWORD 
Depositing User:  MTMT SWORD 
Date Deposited:  03 Nov 2022 11:01 
Last Modified:  03 Nov 2022 11:01 
URI:  http://real.mtak.hu/id/eprint/152853 
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