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.
