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Hazard function analysis for flood planning under nonstationarity
Author(s) -
Read Laura K.,
Vogel Richard M.
Publication year - 2016
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2015wr018370
Subject(s) - weibull distribution , probabilistic logic , exponential distribution , return period , probability density function , log normal distribution , exponential function , hazard , econometrics , distribution fitting , cumulative distribution function , stochastic process , monte carlo method , probability distribution , event (particle physics) , statistics , flood myth , statistical physics , mathematics , physics , mathematical analysis , geography , chemistry , archaeology , organic chemistry , quantum mechanics
The field of hazard function analysis (HFA) involves a probabilistic assessment of the “time to failure” or “return period,” T , of an event of interest. HFA is used in epidemiology, manufacturing, medicine, actuarial statistics, reliability engineering, economics, and elsewhere. For a stationary process, the probability distribution function (pdf) of the return period always follows an exponential distribution, the same is not true for nonstationary processes. When the process of interest, X , exhibits nonstationary behavior, HFA can provide a complementary approach to risk analysis with analytical tools particularly useful for hydrological applications. After a general introduction to HFA, we describe a new mathematical linkage between the magnitude of the flood event, X , and its return period, T , for nonstationary processes. We derive the probabilistic properties of T for a nonstationary one‐parameter exponential model of X , and then use both Monte‐Carlo simulation and HFA to generalize the behavior of T when X arises from a nonstationary two‐parameter lognormal distribution. For this case, our findings suggest that a two‐parameter Weibull distribution provides a reasonable approximation for the pdf of T . We document how HFA can provide an alternative approach to characterize the probabilistic properties of both nonstationary flood series and the resulting pdf of T .