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Chapter 7: Sec 1.7

J

jensen

Member
On page 10, the defination of m_x is given as the probability of a life alive between ages x and x+1 dies.

How different is that from the defination of q_x which I understand is the probability of a life dying between ages x to x+1?
 
Whilst q_x is also known as the 'initial rate of mortality', m_x is the 'central rate of mortality'.

m_x is the annual rate of mortality expressed as a proportion of the average number of people alive during the year of age x.

q_x is the annual rate of mortality expresed as a proportion of the initial number of people alive at age x.

Put into formulas:

q_x = d_x/l_x, where l_x is the number of people alive at the beginning of the year aged x (i.e. the number of survivors at exact age x)

m_x = d_x/L_x, where L_x is the average (in its integral form) value of l_x between ages x and x+1 (i.e. the number of survivors aged x last birthday)

So:
m_x>=q_x as l_x>=L_x

Hope that makes sense.
 
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