Graduation Tests

Question 1

Reasons for Graduation

Answer 1

We expect the true rates to progress smoothly with no irregularities
Graduation reduces sampling error at each age by using information from adjacent ages
Standard Tables are used for premium calculations, where it is important to have unbiased estimates of the true underlying rates
Premuims should vary smoothly with rates(as expect from Policyholder)

Question 2

Null Hypothesis for the graduations Test

Answer 2

The graduated rates are the true underlying mortality rates of the population

Question 3

Drawbacks of the Chi Square Test

Answer 3

Fail to detect large dev if they are offset by many smaller dev
fail to detect overall bias
fail to detect clumping bias

Question 4

Criterion for Graduation

Answer 4

Smoothness
Adherence to data
Suitability

Question 5

Give the 6 graduation test and their purpose

Answer 5

Chi-Square- GoF
Standardised Deviation Test - large difference between the crude rates and graduated rates
GoF and Bias
Sign Test- Bias
Cum Dev Test - overall Bias and GoF
Groupings of the sign test - Bias-clumping of signs
Serial Correlation Test - Serial Correlation