# Maximum Likelihood

1. Dec 25, 2009

### ryusukekenji

http://bbs.mathchina.com/usr1PvjRWKew/4/22/graph_1261406609.jpg [Broken]

I cant understand the equation, may I know is there any good idea to get the value of ξ?

Last edited by a moderator: May 4, 2017
2. Dec 25, 2009

### SW VandeCarr

It is a little hard to read, but based on the curve and the Fig 1 label underneath , it looks like the values of $$\xi$$are plotted on the horizontal axis.

Last edited: Dec 25, 2009
3. Dec 25, 2009

### ryusukekenji

http://cos.name/bbs/attachment/Mon_0912/15_88059_ae128f170c6c431.jpg [Broken]

φ=non-increase function
tk=Time of observation k
I have built up may basic model, while just leaving decay speed ζ which I have no idea...

Last edited by a moderator: May 4, 2017
4. Dec 25, 2009

### SW VandeCarr

Sorry. I didn't know you wanted to derive a value for a parameter of $$\xi$$. I took $$\xi$$ as given and thought we were asking about Maximum Likelihood Estimation.

5. Dec 25, 2009

### ryusukekenji

I didnt stated whole model at first, thats why.....
hmmm... It must apply Maximum Likelihood in order to get ζ ... but I am not really understand α and β which are probabilities of occurrence.

6. Dec 26, 2009

### HallsofIvy

Staff Emeritus
You still haven't told us what the problem really is! If it is to find the maximum likliehood estimator of $\zeta$ from the graph, then it looks to me like the maximum value on the graph occurs around $\zeta= 0.006$.

7. Dec 26, 2009

### ryusukekenji

Example：

T1 T2 X Y Date
A B 1 0 01Jan
A C 2 2 03Jan
B D 3 1 03Jan
A D 1 1 08Jan
B C 0 0 08Jan
C B 2 1 09Jan
D A 1 0 14Jan
D B 2 3 15Jan
C A 2 1 15Jan
B A 1 1 18Jan

I have a dataset of observations on robot soccer competition. Right here I try to stated example above if let say I would like to count team scoring ability through individual double poisson with time series. Previous matches result will less effect through decay function.
The picture above is one of my reference, I would like to follow this paper's weighting function but I am not really know how to get the maximum likelihood of decay rate ζ.