*School of Statistics and Actuarial Science (Journal Articles)
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Item Survival analysis of bank loans in the presence of long-term survivors(South African Statistical Association, 2017-04) Marimo, M; Chimedza, CIn this paper we model competing risks, default and early settlement events, in the presence of long term survivors and compare survival and logistic methodologies. Cause specific Cox regression models were fitted and adjustments were made to accommodate a proportion of long term survivors. Methodologies were compared using ROC curves and area under the curves. The results show that survival methods perform better than logistic regression methods when modelling lifetime data in the presence of competing risks and in the presence of long term survivors.Item Wishart exponential families on cones related to tridiagonal matrices(Springer Tokyo, 2019-04-01) Graczyk, P; Ishi, H; Mamane, SLet G be the graph corresponding to the graphical model of nearest neighbor interaction in a Gaussian character. We study Natural Exponential Families (NEF) of Wishart distributions on convex cones Q G and P G , where P G is the cone of tridiagonal positive definite real symmetric matrices, and Q G is the dual cone of P G . The Wishart NEF that we construct include Wishart distributions considered earlier for models based on decomposable(chordal) graphs. Our approach is, however, different and allows us to study the basic objects of Wishart NEF on the cones Q G and P G . We determine Riesz measures generating Wishart exponential families on Q G and P G , and we give the quadratic construction of these Riesz measures and exponential families. The mean, inverse-mean, covariance and variance functions, as well as moments of higher order, are studied and their explicit formulas are given. © 2018, The Institute of Statistical Mathematics, Tokyo.