Central Rates of Mortality

Dear All,
I can't get the idea of Central Rates of Mortality (mx).

Please refer to the Section 1.8 of Chapter 07. (Survival Models) of the study material. Can you kindly tell me the significance of it. I am not getting the idea written. [Study Material Says: "This represents the probability that a life alive between ages x and X+1 dies."]

Please help.
Regards,
Sumon

 

qx is the initial rate of mortality. This measures the number of deaths divided by the number of lives alive at age x. The problem with this is that it assumes that there are "lx" person years lived between age x->x+1 (Obviously lives will die durring the year of age, and not be exposed to risk for the whole year). mx is the same thing, but it is dx divided by the expected number of person years lived between ages x->x+1. This is Integral from 0-1 l_x+t dt. The meaning of the two is very different. qx is the probability a life now aged x dies within the next year given alive at time x. mx is the probability a life aged anywhere between x,x+1 dies before attaining age x+1. I dont think it's used very much in actuarial calculations but it is handy in dermograpic/population studies because of the nice property that mx * ExC for any age equals the number of deaths, this is not true for qx (Try this for yourself).