- #1
DKOli
- 8
- 0
For censored data.
Random sample X1,...,Xn
Censored such that x1,...xm are observed but xm+1,...,xn are not - we just know they exceed T.
fx = exponential = theata exp(-theta.x)
L = ∏ (from 1 going to m) f(x;theta) ∏ (m+1 - n) 1 - F(T;theta)
Using F = int f I get
L = ∏∅exp(-∅x) ∏ exp(-∅T)
I can now work out the MLE but I want to use EM method.
Reading online I get that this censor (or right censor) would give E(X|X≥T) = T + 1/∅ and I get it but don't really know how to show it. I am not sure how to write the complete data likelihood or log-likelihood for this EM (im more used to mixed distributions or id just solve MLE).
I just don't really know how to set up the E step or M step. It should be quite trivial given what I know already but I just keep confusing myself with the whole
Q(∅,∅i) = E[l(∅;x1,...,xn)|∅i;x1,...,xm).
i have some intial data and then iterating using the M step should also be trivial, I am just falling down at the one of the first hurdles.
Thanks in advance.
Random sample X1,...,Xn
Censored such that x1,...xm are observed but xm+1,...,xn are not - we just know they exceed T.
fx = exponential = theata exp(-theta.x)
L = ∏ (from 1 going to m) f(x;theta) ∏ (m+1 - n) 1 - F(T;theta)
Using F = int f I get
L = ∏∅exp(-∅x) ∏ exp(-∅T)
I can now work out the MLE but I want to use EM method.
Reading online I get that this censor (or right censor) would give E(X|X≥T) = T + 1/∅ and I get it but don't really know how to show it. I am not sure how to write the complete data likelihood or log-likelihood for this EM (im more used to mixed distributions or id just solve MLE).
I just don't really know how to set up the E step or M step. It should be quite trivial given what I know already but I just keep confusing myself with the whole
Q(∅,∅i) = E[l(∅;x1,...,xn)|∅i;x1,...,xm).
i have some intial data and then iterating using the M step should also be trivial, I am just falling down at the one of the first hurdles.
Thanks in advance.