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13_AS_4a_lec_a

# 13_AS_4a_lec_a - Actuarial Statistics Module 4a Parametric...

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Actuarial Statistics – Module 4a: Parametric models: Introduction to more advanced parametric models Actuarial Statistics Benjamin Avanzi c ± University of New South Wales (2012) School of Risk and Actuarial Studies [email protected] Module 4a: Parametric models: Introduction to more advanced parametric models 1/15

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Actuarial Statistics – Module 4a: Parametric models: Introduction to more advanced parametric models Plan 1 Linear log-time model 2 Accelerated failure-time model 3 Relationship between the log-time and accelerated failure-time models 4 Examples 2/15
Actuarial Statistics – Module 4a: Parametric models: Introduction to more advanced parametric models Linear log-time model 1 Linear log-time model 2 Accelerated failure-time model 3 Relationship between the log-time and accelerated failure-time models 4 Examples 3/15

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Actuarial Statistics – Module 4a: Parametric models: Introduction to more advanced parametric models Linear log-time model Linear model representation in log time Notation: X denote the time to the event of interest (eg lifetime) Z = ( z 1 , ··· , z p ) is a vector of explanatory covariates We assume a linear relationship between the log of time ( X ) and covariates Z , such that Y = log X = μ + β Z T + σ W , where β = ( β 1 , , β p ) represent the regression coeﬃcients, and W is the error distribution (that is where the diﬀerence is between models). 3/15
Actuarial Statistics – Module 4a: Parametric models: Introduction to more advanced parametric models Accelerated failure-time model 1 Linear log-time model 2 Accelerated failure-time model 3 Relationship between the log-time and accelerated failure-time models 4 Examples 4/15

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Actuarial Statistics – Module 4a: Parametric models: Introduction to more advanced parametric models Accelerated failure-time model Accelerated failure-time model representation Here we use the idea of modifying a baseline model (with survival function S 0 ). This model is then scaled up or down based on the covariates. The survival function then becomes S ( x ; z ) = S 0 ± x exp h θ Z T , where θ = ( θ 1 , ··· , θ p ) is a vector of regression coeﬃcients.
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13_AS_4a_lec_a - Actuarial Statistics Module 4a Parametric...

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