Flood Frequency Analysis Using the Cox Regression Model
- 1 June 1986
- journal article
- Published by American Geophysical Union (AGU) in Water Resources Research
- Vol. 22 (6) , 890-896
- https://doi.org/10.1029/wr022i006p00890
Abstract
Procedures for incorporating time‐varying exogenous information into flood frequency analyses are developed using the Cox regression model for counting processes. In this statistical model the probability of occurrence of a flood peak in a short interval [t,t+dt) depends in an explicit manner on the values attofk“covariate” processesZ1, …,Zk. Specifically, lettingdN(t) be 1 if a flood peak occurs in [t,t+dt) and 0 otherwise,dN(t) =a(t) exp {∑j=1kbjZj(t)} +dM(t) wherea, the “baseline intensity,” is an unknown function,bis a vector of unknown “regression” parameters, and the errordM(t) is (conditionally) orthogonal to the past history. Two applications, assessment of relative importance of physical processes such as snow melt or soil moisture storage on flood frequency at a site and derivation of time‐varying flood frequency estimates, are considered.This publication has 16 references indexed in Scilit:
- Markov Flow Models and the Flood Warning ProblemWater Resources Research, 1985
- Statistical Inference for Point Process Models of RainfallWater Resources Research, 1985
- Maximum Likelihood Estimates for the Parameters of Mixture DistributionsWater Resources Research, 1984
- The martingale method: Introductory sketch and access to the literatureOperations Research Letters, 1984
- Understanding Cox's Regression Model: A Martingale ApproachJournal of the American Statistical Association, 1984
- Threshold Methods for Sample ExtremesPublished by Springer Nature ,1984
- A cluster model for flood analysisWater Resources Research, 1983
- Cox's Regression Model for Counting Processes: A Large Sample StudyThe Annals of Statistics, 1982
- Two extreme value processes arising in hydrologyJournal of Applied Probability, 1976
- Partial likelihoodBiometrika, 1975