Modeling hydro-meteorological variables from heterogeneous populations using mixture distributions

Abstract

Mixture distributions have been widely used for modeling hydrometeorological variables resulting from more one generating mechanisms. However, a small number of studies has employed the mixture distributions for modeling hydrometeorological variables. It is still required to explore the capacity of the mixture distribution for modeling various hydro-meteorological variables in order to improve our understanding of the hydro-meteorological variables. In the current thesis, the mixture distribution indicates an additive mixture model that a probability distrbituion is a weighted sum of component densities. The applicabilities of various mixture distributions are investigated, and their suitabilities are compared with conventional non-mixture distributions for various variables. The mixture distributions lead to improvements in modeling extreme rainfalls, wind speeds, floods, and simulated data. The mixture distributions provide chances to model the data that non-mixture distributions cannot model and more information than the non-mixture distributions. The performances of the seasonal maximum mixture models are compared to the performance of the additive mixture models. Thirty-six seasonal maximum mixture models and ten additivemixture models are employed, and their fits are compared. The characteristics of seasonal maximum mixture models are discussed. Overall, the additive mixture models lead to better fits than the seasonal maximum mixture models for annual maximum series based on the employed goodness-of-fit measures. According to the simulation results, the seasonal maximum mixture models can represent uncertainties that cannot be modeled by the additive model. When seasonal maximum serires are available, the SM should be employed to model extreme events. The nonstationary mixture distribution is proposed for modeling hydro- meteorological variables simultaneously taking into consideration multiple generating mechanisms and nonstationarity. The proposed nonstationary mixture distributions assume that location parameters of the component densities are functions of time covariate. For fitting the proposed nonstationary mixture distributions, a new parameter estimation method of the nonstationary mixture distribution is proposed. The performance of the proposed method is assessed by a simulation study. According to the simulation results, the proposed method successfully fit the proposed models. For comparison, nonstationary generalized extreme value (GEV) distributions are employed. The fits of the proposed nonstationary mixture distribution can be comparable to the fits of the nonstationary GEV distributions. The proposed models can interpret the information that the nonstationary GEV cannot detect

Date of Award	Dec 2016
Original language	American English
Supervisor	Taha B. M. J. Ouarda (Supervisor)