Transcript A Life Table Discussion Topic

A Life Table
Discussion Topic
(Session 14)
SADC Course in Statistics
Learning Objectives – this session
At the end of this session, you will be able to
• explain some further summaries of
survivorship data in Life Tables
• discuss some issues relating to the
application of Life Table methodology
• think constructively about approaches to
new practical applications of Life Table ideas
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Introduction
“Wikipedia” is a public-domain web resource
with articles contributed voluntarily by the
readership. In August 2007 search for “Life
Table” produced definitions given below &
an interesting diagram, reproduced below.
The summary description of the diagram was
incomprehensible, so this session focuses on
studying the diagram, & figuring out how to
reproduce and explain what it shows.
See
http://en.wikipedia.org/wiki/Life_table
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New LT summaries
As well as qx, px = 1-qx, lx and dx the article
introduces tpx: the probability that someone
aged exactly x will survive for t more years,
& t|kqx: the probability that someone aged
exactly x will survive for t more years, then
die within the next k years.
Why would someone want to know this?
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Insurers’ interests
If a man of working age x takes out an
annuity-based pension from an insurer, the
insurance deal might be that:• he pays premiums for t more years till he
reaches retirement age,
• if he survives longer the insurer pays him
an annual sum for the rest of his life, or
• if he dies before retirement his premiums
are lost
So insurer would want to estimate
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t|kqx
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The Wikipedia illustration
FOR CLASSROOM DISCUSSION BY YOU,
facilitated by your trainer:The illustration shown in the web reference is
the following diagram of various values of
tpx with x-values being the age scale (xaxis) and each curve showing a different
minimum survival time t in a different
colour.
The data depicted draw on a 2003 Life Table
for the total population of the US
http://upload.wikimedia.org/wikipedia/commons/b/be/Excerpt_from_CDC_2003_Table_1.png
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Q.1
The added lines shown on the diagram read off
a value of about 0.87 corresponding to x = 40.
What
isyour
your
interpretation
of and
this
point?
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Q.2
The added lines shown on the diagram read off
a value of about 0.89 corresponding to x = 50.
What
isyour
your
interpretation
of and
this
point?
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Q.3
Give your explanation as to why the second
value above (0.89) is higher than the first
(0.87). Discuss!
Note that the values given above are roughly
read off from the graphs shown. They
have not been computed.
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Q.4
The added line shown on the diagram reads off
5 values corresponding to x = 60. What is
your
interpretation
ofView
this
set and
of Footer
values?
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Q.5
The added line shown on the diagram reads off
5 values corresponding to tpx = 0.5. What is
your
interpretation
ofView
this
set and
of Footer
values?
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Q.6
In terms of LT “algebra” can you discuss,
agree and write down the formula for:tpx: the probability that someone aged
exactly x will survive for t more years, &
Q.7
In terms of LT “algebra” can you discuss,
agree and write down the formula for:t|kqx: the probability that someone aged
exactly x will survive for t more years, then
die within the next k years?
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Q.8
Why would it be very difficult to produce a
diagram like the above? for t|kqx?
Q.9
An insurance company wants a set of
illustrations of t|kqx in order to familiarise
its annuity sales staff with the way its
annuity policies work. Discuss what
graphs you think it might be worth
producing, and how you would explain
them.
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Some practical work follows …
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