Abstract:
As a generalization of the commonly assumed Poisson distribution (PD) used to estimate the annual
number of peaks over threshold in partial duration series (PDS) model, the negative binomial (NB) distribution
is proposed in this study. Instead of generalized pareto distribution (GPD) and exponential distribution
(ED) models popularly applied to predict the probability of the exceedances of peak over
threshold, the performance of the general logistic distribution (GLD) models is analyzed. Two different
models for analyzing extreme hydrologic events are compared, based on, PDS and annual maximum series
(AMS), respectively. The performance of the two models in terms of uncertainty of T-year event estimator
[q(T)] is evaluated in the cases of estimation with the method of moments (MOMs), maximum
likelihood (ML), and probability weighted moments (PWMs). The annual maximum distribution corresponding
to a PDS model with Poisson distributed count of peaks above threshold and GLD for flood
exceedances was found to be an extreme value type I (EV1) distribution. The comparison between PDS
and AMS is made using ratio of variance of the T-year event estimates, which is derived analytically after
checking the reliability of the expressions with Monte Carlo simulations. The results reveal that the AMS/
NB–GLD and PDS/GLD models using PWM estimation method give least variance of flood estimates with
the PDS model giving marginally better results. From the overall results, it was observed that the Poisson
distribution performs better, where the difference between mean (l) and variance of counts of threshold
exceedances is small otherwise the NB distribution is found to be efficient when used in combination
with generalized logistic distribution in the PDS model, and this is more prominent for l < 1.4. Hence,
in such cases when the PDS data have a mean less than this, the AMS/NB–GLD and PDS/GLD should be
a better model for q(T) estimation as compared to PDS/ED.
