Page 130 - Contributed Paper Session (CPS) - Volume 3

CPS1970 Nurul Aityqah Y. et al.
was better met and the problem associated with violation of this assumption
was avoided.

2. Methodology
The data sets used in this study were obtained from the Department of
Statistics Malaysia (DOSM) and it consists of Malaysia mortality (Peninsular
Malaysia, Sabah and Sarawak) for the period of 1991 to 2015. The mortality
data for female, male and total population will measure by age-specific death
rates (ASDR). The ASDR is calculated as , = ⁄ , , where , is the
,
number of deaths for a group of ages in year and is the observed
,
population (exposure to risk) for a group of ages in year . The data set
consist of ASDR for 19 age groups which are organized into 5-year intervals
such as 0, 1-4, 5-9… 85+.
The LC model is as follows:

ln( ) = + , + = 0, … . . , = 1, … , (1)
,
,

where is the age-specific death rate for the interval and the year , is
,

the mortality index in the year , is the average age-specific mortality, is

a deviation in the mortality due to changes in the index and is the
,

random error.
As the solution is not possible to be unique, the following constraints were
imposed (Lee. & Carter, 1992):

1
= ∑ ( ) (2)
,

= 1

∑ = 1 (3)

= 1

∑ = 0 (4)

= 1

Applying SVD to the matrix
= ( ) − ̃ (5)

,

produced
= ( ) = + ⋯ + (6)
′

1 1 1

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