Thesis (Ph.D. (Statistics)) -- University of Limpopo, 2022 / This thesis is based on application of frailty and copula models to under five child mortality data set in South Africa. The main purpose of the study was to apply sample splitting techniques in a survival analysis setting and compare clustered survival models considering left truncation to the under five child mortality data set in South Africa. The major contributions of this thesis is in the application of the shared frailty model and a class of Archimedean copulas in particular, Clayton-Oakes copula with completely monotone generator, and introduction of sample splitting techniques in a survival analysis setting. The findings based on shared frailty model show that clustering effect was sig nificant for modelling the determinants of time to death of under five children, and revealed the importance of accounting for clustering effect. The conclusion based on Clayton-Oakes model showed association between survival times of children from the same mother. It was found that the parameter estimates for the shared frailty and the Clayton-Oakes models were quite different and that the two models cannot be comparable. Gender, province, year, birth order and whether a child is part of twin or not were found to be significant factors affect ing under five child mortality in South Africa. / NRF-TDG Flemish Interuniversity Council Institutional corporation (VLIR-IUC) VLIR-IUC Programme of the University of Limpopo