A
Ark raw
Member
- why is the force of mortality μ_x defined as, μ_x =-d(lnl_x)/dx ?
Thank You.
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I've read that section it doesn't explain the reason behind this definition.For your first question, have you read Section 1.3 of Chapter 3? - it is fully explained there. Let me know if this does not explain it for you.
I've read that section it doesn't explain the reason behind this definition.
Will keep this in my mind.As here it very helpful if you make your question as clear as possible - this will help others to answer your queries as well as me - particularly as you are asking quite a lot of questions
Thank you for clarifying your question
mu_x is the annual rate at which a person aged x is dying at exact age x.
P[T=<x+h|T>x] is the probability that a life who is aged x dies in the next h of a year.
Suppose h was 1 day (= 1/365 of a year). And say the probability of dying in this period was 0.00004. If we divide this by h, we get the annual rate at which the person is dying over that single day. So this person is dying at an annual rate of 0.00004/(1/365) = 0.0146 pa over this single day.
By taking h to be a smaller and smaller time period we end up with the annual rate at which the person is dying at the current instant of time (ie at exact age x) - which is what mu_x is.
As here it very helpful if you make your question as clear as possible - this will help others to answer your queries as well as me - particularly as you are asking quite a lot of questions!
Thank you!
Robert