Actuarial Models Coursework

Project description
Only the Exercise 4 in the coursework doc I have attached, its not a very hard one and it shouldn’t take long. I have attached both the lecture notes and the question. The question is Exercise 4 and I have paste it here but please open the coursework doc for a clear version.

Exercise 4:

Table 2 gives the observed times in years until divorce since marriage of 20 couples. Some of the observed couples were still married at the end of the study, while for some other couples one of the spouses died while still being married. The observations corresponding to those couples are indicated by a .
1.5 2 2 2 3 3.5 3.5 4 4 4 6 6 6.5 7 9 12 14 14 15 17
Table 2: Table corresponding to Exercise 4.

(a)
(i) Determine the Kaplan-Meier estimator.
(ii) Using the Kaplan-Meier estimator, estimate the probability that a couple divorces
before they reach their 5-year anniversary.
(b)
Assume now that the hazard function is of the following piecewise constant form:
the hazard is equal to 1 for the first 5 years after marriage,
the hazard is equal to 2 between 5 and 10 years after marriage,
the hazard is equal to 3 after 10 years of marriage.
(i) Find the maximum likelihood estimates of 1, 2 and 3.

(ii) Using this parametric distribution, estimate the probability that a couple who
have been married for exactly 4 years, will not be divorced 5 years later.

(iii) Use an appropriate test to see whether this parametric distribution provides a
better fit at the 5% significance level than the exponential distribution.

(c)
Suppose you want to estimate the expected duration of a marriage (until divorce)
corresponding to the data in Table 2. What estimator would you use for this, the
parametric one or the non-parametric one, or does it not matter? Explain your
answer

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