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A Note on Exact Laws of Large Numbers for Asymmetric Pareto-type Distributions with Applications to Ratios of Random Variables

Vol. 15 No. 2 (2020) P.177~P.186
 DOI: https://doi.org/10.21915/BIMAS.2020205 10.21915/BIMAS.2020205

ABSTRACT

We prove some unusual limit laws for weighted sums of i.i.d. random variables with asymmetric Pareto-type distributions. The obtained results are applied to the convergence of ratios of independent random variables.

KEYWORDS
law of large numbers, i.i.d. random variables, ratios of random variables

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 60F15, 60F05, 60G50

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