An iterative parametric estimation method for Hammerstein large-scale systems: a simulation study of hydraulic process

Given $(Z_{i},\delta _{i})=\left\{ \min (T_{i},C_{i}),I_{(T_{i}<C_{i})_{i=1,2}}\right\} ,$ as dependent or independent right-censored variables, general formulas are proven for a semi-parametric estimation of the proposed method. As a logical continuation of results established by N.IDIOU et al 2021 \cite{ref16}, a new estimator of $\tilde{C}$ is proposed by considering that the underlying copula is Archimedean, under singly censoring data. As an application, two Archimedean copulas models have been chosen to illustrate our theoretical results. A simulation study follows, which sheds light on the behavior of the process estimation method shown that the proposed estimator performs well in terms of relative bias and RMSE. The methodology of the proposed estimator is also illustrated by using lifetime data from the Diabetic Retinopathy Study, where its efficiency and robustness are observed.

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Frequency Analysis of Nonidentically Distributed Hydrometeorological Extremes Associated with Large-Scale Climate Variability Applied to South Korea

Journal of Applied Meteorology and Climatology ◽

10.1175/jamc-d-13-0200.1 ◽

2014 ◽

Vol 53 (5) ◽

pp. 1193-1212 ◽

Cited By ~ 8

Author(s):

Taesam Lee ◽

Changsam Jeong

Keyword(s):

Parameter Estimation ◽

Climate Variability ◽

South Korea ◽

Simulation Study ◽

Extreme Events ◽

Large Scale ◽

Southern Oscillation ◽

Estimation Method ◽

Parameter Estimation Method

AbstractIn the frequency analyses of extreme hydrometeorological events, the restriction of statistical independence and identical distribution (iid) from year to year ensures that all observations are from the same population. In recent decades, the iid assumption for extreme events has been shown to be invalid in many cases because long-term climate variability resulting from phenomena such as the Pacific decadal variability and El Niño–Southern Oscillation may induce varying meteorological systems such as persistent wet years and dry years. Therefore, the objective of the current study is to propose a new parameter estimation method for probability distribution models to more accurately predict the magnitude of future extreme events when the iid assumption of probability distributions for large-scale climate variability is not adequate. The proposed parameter estimation is based on a metaheuristic approach and is derived from the objective function of the rth power probability-weighted sum of observations in increasing order. The combination of two distributions, gamma and generalized extreme value (GEV), was fitted to the GEV distribution in a simulation study. In addition, a case study examining the annual hourly maximum precipitation of all stations in South Korea was performed to evaluate the performance of the proposed approach. The results of the simulation study and case study indicate that the proposed metaheuristic parameter estimation method is an effective alternative for accurately selecting the rth power when the iid assumption of extreme hydrometeorological events is not valid for large-scale climate variability. The maximum likelihood estimate is more accurate with a low mixing probability, and the probability-weighted moment method is a moderately effective option.

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