Undersampling power-law size distributions: effect on the assessment of extreme natural hazards

Eric Geist () and Tom Parsons

Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, 2014, vol. 72, issue 2, 565-595

Abstract: The effect of undersampling on estimating the size of extreme natural hazards from historical data is examined. Tests using synthetic catalogs indicate that the tail of an empirical size distribution sampled from a pure Pareto probability distribution can range from having one-to-several unusually large events to appearing depleted, relative to the parent distribution. Both of these effects are artifacts caused by limited catalog length. It is more difficult to diagnose the artificially depleted empirical distributions, since one expects that a pure Pareto distribution is physically limited in some way. Using maximum-likelihood methods and the method of moments, we estimate the power-law exponent and the corner size parameter of tapered Pareto distributions for several natural hazard examples: tsunamis, floods, and earthquakes. Each of these examples has varying catalog lengths and measurement thresholds, relative to the largest event sizes. In many cases where there are only several orders of magnitude between the measurement threshold and the largest events, joint two-parameter estimation techniques are necessary to account for estimation dependence between the power-law scaling exponent and the corner size parameter. Results indicate that whereas the corner size parameter of a tapered Pareto distribution can be estimated, its upper confidence bound cannot be determined and the estimate itself is often unstable with time. Correspondingly, one cannot statistically reject a pure Pareto null hypothesis using natural hazard catalog data. Although physical limits to the hazard source size and attenuation mechanisms from source to site constrain the maximum hazard size, historical data alone often cannot reliably determine the corner size parameter. Probabilistic assessments incorporating theoretical constraints on source size and propagation effects are preferred over deterministic assessments of extreme natural hazards based on historical data. Copyright US Government 2014

Keywords: Extreme natural hazards; Catalog; Empirical; Power law; Undersampling; Pareto; Probability (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://hdl.handle.net/10.1007/s11069-013-1024-0 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:nathaz:v:72:y:2014:i:2:p:565-595

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/11069

DOI: 10.1007/s11069-013-1024-0

Access Statistics for this article

Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards is currently edited by Thomas Glade, Tad S. Murty and Vladimír Schenk

More articles in Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards from Springer, International Society for the Prevention and Mitigation of Natural Hazards
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().