||The thesis studies mathematical and statistical properties of the generalized Farlie-Gumbel-Morgenstern (FGM) copula (Bairamov and Kotz 2002). The first part of the thesis reviews several properties of dependence measures (Spearman’s rho, Kendall’s tau, Kochar and Gupta’s dependence measure, and Blest’s coefficient) under the generalized FGM copula. We give a few remarks on the relationship among the dependence measures, derive Blest’s coefficient, and suggest simplifying the previously obtained expression of Kochar and Gupta’s dependence measure. The second part of the thesis considers dependent competing risks analysis under the generalized FGM copula model. We obtain the expression of sub-distribution functions under the generalized FGM copula model, which has not been discussed in the literature. With the Burr III margins, we show that our expression has a closed form and generalizes the reliability measure previously obtained by Domma and Giordano (2013). We develop maximum likelihood estimation under the proposed competing risks models with a randomized Newton-Raphson algorithm for numerical maximization. We conduct simulations to check the correctness of our method and analyze a real dataset for illustration.|
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