Between exact age 70 and exact age 71 bi di ti life i

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: s Binomial model With censoring Example In a mortality investigation, the following data have been recorded for 6 independent lives observed between exact age 70 and exact age 71. bi di ti Life i ai 1 0 1 0 2 0.3 0.9 0 3 0.5 1 1 0.9 4 0 0.4 0 5 0 0.9 1 0.7 6 0 1 1 0.8 Using the Binomial Model of Mortality the likelihood of these observations is LB = p70 × 0.6 p70.3 × 0.5 q70.5 × 0.4 p70 × 0.9 q70 × q70 8/30 Actuarial Statistics – Module 6: Parametric models: Binomial and Poisson models Binomial model The actuarial estimate 1 Binomial model Without censoring With censoring The actuarial estimate Central exposed to risk Discussion 2 Poisson model Introduction Maximum Likelihood Estimation Link to 2-state Markov models 3 Discussion: Binomial, Poisson and Markov multi-state models 9/30 Actuarial Statistics – Module 6: Parametric models: Binomial and Poisson models Binomial model The actuarial estimate The actuarial estimate Let D be the number of deaths ( N i =1 Di ). We have then N E [D ] = (bi −ai qx +ai ) i =1 Now note that bi −ai qx +ai = Pr ith life dies between x + ai and x + bi = Pr ith life dies between x + ai and x + 1 − Pr ith life dies between x + bi and x + 1 = 9/30 1−ai qx +ai − (bi −ai px +ai ) (1−bi qx +bi ) Actuarial Statistics – Module 6: Parametric models: Binomial and Poisson models Binomial model The actuarial estimate Furthermore, using Balducci assumption and 1−bi qx +bi = (1 − bi ) qx we obtain 1−ai qx +ai = (1 − ai ) qx N...
View Full Document

This document was uploaded on 04/03/2014.

Ask a homework question - tutors are online