7. The following 4-state Markov model with constant intensities a, ß and y is used to model a pension scheme for male members aged 55. Age is defined as age last birthday on January 1". The states are w: Active, a: Preserved Benefit, b: Drawing pension and d: Dead. The following data were collected over an observation period covering a single calendar year on 1000 male members of the above pension scheme, all of whom are aged 55: Total waiting time in state w: 800 years Total number of transfers from state w to state a: 200 Total number of transfers from state w to state b: 200 Total number of transfers from state w to state c: 20 Find the likelihood function L(a, B.y) for these data and hence find the maximum likelihood estimates of a,ß and y.
7. The following 4-state Markov model with constant intensities a, ß and y is used to model a pension scheme for male members aged 55. Age is defined as age last birthday on January 1". The states are w: Active, a: Preserved Benefit, b: Drawing pension and d: Dead. The following data were collected over an observation period covering a single calendar year on 1000 male members of the above pension scheme, all of whom are aged 55: Total waiting time in state w: 800 years Total number of transfers from state w to state a: 200 Total number of transfers from state w to state b: 200 Total number of transfers from state w to state c: 20 Find the likelihood function L(a, B.y) for these data and hence find the maximum likelihood estimates of a,ß and y.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:7. The following 4-state Markov model with constant intensities a, B and y is used to model
a pension scheme for male members aged 55. Age is defined as age last birthday on
January 1". The states are w: Active, a: Preserved Benefit, b: Drawing pension and d: Dead.
The following data were collected over an observation period covering a single calendar year
on 1000 male members of the above pension scheme, all of whom are aged 55:
Total waiting time in state w: 800 years
Total number of transfers from state w to state a: 200
Total number of transfers from state w to state b: 200
Total number of transfers from state w to state c: 20
Find the likelihood function L(a, B.y) for these data and hence find the
maximum likelihood estimates of a,ß and y.
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