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Chapter 2 Survival models Manual for SOA Exam MLC Chapter 2 Survival models Section 2 7 Common Analytical Survival Models c 2009 Miguel A Arcones All rights reserved Extract from Arcones Manual for SOA Exam MLC Fall 2009 Edition available at http www actexmadriver com 1 27 c 2009 Miguel A Arcones All rights reserved Manual for SOA Exam MLC Chapter 2 Survival models Section 2 7 Common Analytical Survival Models Common Analytical Survival Models Sometimes it is of interest to assume that the survival function follows a parametric model i e it is of the form S x where is an unknown parameter There are several reasons to make this assumption 1 Data supports this assumption Actuaries realized that the models observed in real life follow this assumption 2 Computations are simpler using a parametric model 3 There are valid scientific reasons to justify the use of a particular parametric model 2 27 c 2009 Miguel A Arcones All rights reserved Manual for SOA Exam MLC Chapter 2 Survival models Section 2 7 Common Analytical Survival Models The most common approach is not to use parametric models due to the following reasons 1 Modern computers allow to handle the computations needed using the collected data 2 It is difficult to justify that a parametric model applies 3 Knowing that a particular model applies we can get more accurate estimates But this increase in accuracy is not much If a parametric model does not apply using the parametric approach we can get much worse estimates than the nonparametric estimates 3 27 c 2009 Miguel A Arcones All rights reserved Manual for SOA Exam MLC Chapter 2 Survival models Section 2 7 Common Analytical Survival Models De Moivre model De Moivre s law 1729 assumes that deaths happen uniformly over the interval of deaths i e the density of the age at failure is fX x 1 for 0 x Therefore x for 0 x x FX x for 0 x 1 x for 0 x x s x t x t for 0 t x t px s x x t for 0 t x t qx x SX x 4 27 c 2009 Miguel A Arcones All rights reserved Manual for SOA



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