Advantages of graduation: By parametric formula with reference to a standard table.using a graphical method.....

(i) By parametric formula with reference to a standard table using a graphical method. [4]

(ii) Outline the steps involved in graduating mortality rates with reference to a
standard table [3]

i) Parametric formula

The resultant graduation will be sufficiently smooth provided few parameters are used. [1]
It is a suitable method to produce standard tables. [½]
It can be useful to fit the same formula to several experiences to give insight into the differences between experiences. [½]
Reference to a standard table It can be used to fit relatively small data sets in cases where a suitable standard
table exists. [1]
The graduated rates should be smooth provided that a simple function is used.
[1]
The standard table can provide information at extreme ages where data may be
scanty

OR

The shape of the table can be used to “fill in gaps” in the data [½]

It can be useful to fit the same table to several experiences with the same link function to give insight into how the experience differs over time. [½]
Graphical graduation It can be used for scanty data sets where no suitable standard table exists

OR

no more sophisticated method is justifiable. [1]
It enables an experienced analyst to allow for known (or likely) features of the
data. [½]

It can give a quick initial feel for the rates. [½]
[Total for part (i): max. 4]

(ii)

Select a suitable standard table. [½]
In making this selection, consider the nature of lives of involved, and compare their characteristics with the description of data used in a range of standard tables; and [½]
the date range for information used in preparation of the standard tables, with a general preference for using data closer in date to the period for the crude
rates if possible. [½]
Select one or more link functions to try. [½]
Exploratory graphical or regression analysis may help with the selection of the link function. [½]
Estimate the parameters [½]
using a method such as maximum likelihood or least squares. [½]
Compute the graduated rates. [½]
Perform statistical tests on the graduation to check adherence to the data. [½]
If necessary, repeat some or all steps until satisfied with graduation. [½]
[Total for part (ii): max. 3]

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emanuelleipa answered the question on October 15, 2019 at 20:05

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