Bi di ti life i ai 1 0 1 0 2 03 09 0 3 05 1 1 09 4 0

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: ∂µ µ leads to the estimator D µ= c ˜ Ex Actuarial Statistics – Module 6: Parametric models: Binomial and Poisson models Poisson model Maximum Likelihood Estimation 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 Poisson Model of Mortality and assuming a constant force of mortality, µ70 over (70, 71), find MLE of q70 . 21/30 Actuarial Statistics – Module 6: Parametric models: Binomial and Poisson models Poisson model Maximum Likelihood Estimation Solution We have c E70 = 1 + 0.6 + 0.4 + 0.4 + 0.7 + 0.8 = 3.9 If one writes µ for µ70 , the likelihood is then LP = (3.9µ)3 e −3.9µ 3! with log log LP = 3 log µ − 3.9µ + 3 log 3.9. Differentiating log LP with respect to µ, setting the derivative to zero and checking second derivative (negative) we get: 3 ˆ µ70 = = 0.769 3.9 Since q70 = 1 − e −...
View Full Document

Ask a homework question - tutors are online