Matches in SemOpenAlex for { <https://semopenalex.org/work/W285266469> ?p ?o ?g. }
- W285266469 endingPage "1228" @default.
- W285266469 startingPage "1187" @default.
- W285266469 abstract "Heavy tailed random variables (rvs) have proven to be an essential element in modeling a wide variety of natural and human-induced processes, and the sums of heavy tailed rvs represent a particularly important construction in such models. Oriented toward both geophysical and statistical audiences, this paper discusses the appearance of the Pareto law in seismology and addresses the problem of the statistical approximation for the sums of independent rvs with common Pareto distribution F(x)=1 − x−α for 1/2 < α < 2. Such variables have infinite second moment which prevents one from using the Central Limit Theorem to solve the problem. This paper presents five approximation techniques for the Pareto sums and discusses their respective accuracy. The main focus is on the median and the upper and lower quantiles of the sum’s distribution. Two of the proposed approximations are based on the Generalized Central Limit Theorem, which establishes the general limit for the sums of independent identically distributed rvs in terms of stable distributions; these approximations work well for large numbers of summands. Another approximation, which replaces the sum with its maximal summand, has less than 10% relative error for the upper quantiles when α < 1. A more elaborate approach considers the two largest observations separately from the rest of the observations, and yields a relative error under 1% for the upper quantiles and less than 5% for the median. The last approximation is specially tailored for the lower quantiles, and involves reducing the non-Gaussian problem to its Gaussian equivalent; it too yields errors less than 1%. Approximation of the observed cumulative seismic moment in California illustrates developed methods." @default.
- W285266469 created "2016-06-24" @default.
- W285266469 creator A5015259550 @default.
- W285266469 creator A5073868501 @default.
- W285266469 creator A5081109064 @default.
- W285266469 date "2005-06-01" @default.
- W285266469 modified "2023-10-17" @default.
- W285266469 title "Approximating the Distribution of Pareto Sums" @default.
- W285266469 cites W1214703565 @default.
- W285266469 cites W134624220 @default.
- W285266469 cites W1486650488 @default.
- W285266469 cites W1498464051 @default.
- W285266469 cites W1515444288 @default.
- W285266469 cites W1523228994 @default.
- W285266469 cites W1535277709 @default.
- W285266469 cites W1556573274 @default.
- W285266469 cites W1564609383 @default.
- W285266469 cites W1577673399 @default.
- W285266469 cites W1890199497 @default.
- W285266469 cites W1904429860 @default.
- W285266469 cites W1960471763 @default.
- W285266469 cites W1964994620 @default.
- W285266469 cites W1966257929 @default.
- W285266469 cites W1970173423 @default.
- W285266469 cites W1975836976 @default.
- W285266469 cites W1984232269 @default.
- W285266469 cites W1998678833 @default.
- W285266469 cites W2007280334 @default.
- W285266469 cites W2017628301 @default.
- W285266469 cites W2022894179 @default.
- W285266469 cites W2027384242 @default.
- W285266469 cites W2042989654 @default.
- W285266469 cites W2045831626 @default.
- W285266469 cites W2056976491 @default.
- W285266469 cites W2074851072 @default.
- W285266469 cites W2078206416 @default.
- W285266469 cites W2107722219 @default.
- W285266469 cites W2108443715 @default.
- W285266469 cites W2110448165 @default.
- W285266469 cites W2120062331 @default.
- W285266469 cites W2127150969 @default.
- W285266469 cites W2149617695 @default.
- W285266469 cites W2151580336 @default.
- W285266469 cites W2152037842 @default.
- W285266469 cites W2152948764 @default.
- W285266469 cites W2157005274 @default.
- W285266469 cites W2159916387 @default.
- W285266469 cites W2162077393 @default.
- W285266469 cites W2165919885 @default.
- W285266469 cites W2279852746 @default.
- W285266469 cites W2491018796 @default.
- W285266469 cites W2507681402 @default.
- W285266469 cites W2751862591 @default.
- W285266469 cites W27965200 @default.
- W285266469 cites W32792475 @default.
- W285266469 cites W367858178 @default.
- W285266469 cites W45326702 @default.
- W285266469 cites W634635050 @default.
- W285266469 cites W70870197 @default.
- W285266469 doi "https://doi.org/10.1007/s00024-004-2666-3" @default.
- W285266469 hasPublicationYear "2005" @default.
- W285266469 type Work @default.
- W285266469 sameAs 285266469 @default.
- W285266469 citedByCount "91" @default.
- W285266469 countsByYear W2852664692012 @default.
- W285266469 countsByYear W2852664692013 @default.
- W285266469 countsByYear W2852664692014 @default.
- W285266469 countsByYear W2852664692015 @default.
- W285266469 countsByYear W2852664692016 @default.
- W285266469 countsByYear W2852664692017 @default.
- W285266469 countsByYear W2852664692019 @default.
- W285266469 countsByYear W2852664692020 @default.
- W285266469 countsByYear W2852664692021 @default.
- W285266469 countsByYear W2852664692022 @default.
- W285266469 countsByYear W2852664692023 @default.
- W285266469 crossrefType "journal-article" @default.
- W285266469 hasAuthorship W285266469A5015259550 @default.
- W285266469 hasAuthorship W285266469A5073868501 @default.
- W285266469 hasAuthorship W285266469A5081109064 @default.
- W285266469 hasBestOaLocation W2852664692 @default.
- W285266469 hasConcept C105795698 @default.
- W285266469 hasConcept C110121322 @default.
- W285266469 hasConcept C118671147 @default.
- W285266469 hasConcept C121332964 @default.
- W285266469 hasConcept C122123141 @default.
- W285266469 hasConcept C122383733 @default.
- W285266469 hasConcept C126255220 @default.
- W285266469 hasConcept C133514767 @default.
- W285266469 hasConcept C134306372 @default.
- W285266469 hasConcept C137635306 @default.
- W285266469 hasConcept C141513077 @default.
- W285266469 hasConcept C147581598 @default.
- W285266469 hasConcept C151201525 @default.
- W285266469 hasConcept C1602530 @default.
- W285266469 hasConcept C163716315 @default.
- W285266469 hasConcept C166785042 @default.
- W285266469 hasConcept C190373308 @default.
- W285266469 hasConcept C28826006 @default.