LARGE DEVIATIONS OF MEANS OF HEAVY-TAILED RANDOM VARIABLES WITH FINITE MOMENTS OF ALL ORDERS
| Autor: | Jaakko Lehtomaa |
|---|---|
| Přispěvatelé: | Department of Mathematics and Statistics |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Hazard (logic) Logarithm large deviation General Mathematics 010102 general mathematics heavy-tailed Logarithmic asymptotics SUMS Function (mathematics) Type (model theory) 01 natural sciences stretched exponential Exponential function 010104 statistics & probability Log-normal distribution 111 Mathematics Large deviations theory regular variation Statistical physics PRINCIPLE 0101 mathematics Statistics Probability and Uncertainty Random variable Mathematics |
| Popis: | Logarithmic asymptotics of the mean process {Sn∕n} are investigated in the presence of heavy-tailed increments. As a consequence, a full large deviations principle for means is obtained when the hazard function of an increment is regularly varying with index α∈(0,1). This class includes all stretched exponential distributions. Thus, the previous research of Gantert et al. (2014) is extended. Furthermore, the presented proofs are more transparent than the techniques used by Nagaev (1979). In addition, the novel approach is compatible with other common classes of distributions, e.g. those of lognormal type. |
| Databáze: | OpenAIRE |
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