# Random no, mle,method of moments

#### tsukiko

##### New Member
Hi.
1. I generate a random sample x=(x1,…,xn) of size n from dist A with parameters (a1,a2) in R.
2. I have a likelihood function which involves another 2 dist B & C with parameters (b1,b2,b3) & (c1,c2) respectively. So, I want to maximize this likelihood to obtain mle of (b1,b2,b3,c1,c2).
3. I use R to solve this. But, I have a problem in getting the initial/starting values of (b1,b2,b3,c1,c2).
a) I’m thinking of using method of moment (henceforth MOM) to get the initial values but I’m not sure on how to do this.
b) Should I apply MOM to dist B & C respectively and then plug in the xi values into those moments function? Does this make sense since xi are coming from A and not B or C?
c) If I apply MOM to dist A, what is the benefit I get from it? I already know and don’t care about (a1,a2) and I believe this is not going to help me getting the hints for (b1,b2,b3,c1,c2) values.
d) As far as I know, we usually apply MOM onto the dist we are interested in estimating its parameter only and usually, this dist is the dist we use to generate the random sample. But, this is not the case we considered here. The dist of interest are B & C but the generated dist are A. So, I think b) or c) are not the right thing to do. Am I right?
e) Or should I apply MOM onto the likelihood function in 2? Can we really find the moments of likelihood? It sounds complicated to me.
f) Anyway, does anyone know how to connect MOM and likelihood function we considered here?
g) Or do you have any ideas on getting the initial values of (b1,b2,b3,c1,c2)?

Correct me if any of my belief above is wrong.I really need advice/opinion regarding this matter and any help will be really appreciated. Thanks in advanced.

#### mp83

##### TS Contributor
The sirst step is a generation step. For the rest of the problem it will be disregarded.

#### tsukiko

##### New Member
The sirst step is a generation step. For the rest of the problem it will be disregarded.

Sorry, what do you mean? My first step is wrong?

#### mp83

##### TS Contributor
No, I mean that after this step is completed then for the rest of the procedure you proceed as you never generated them.

In fact this is as if you have a random sample from a apopulation that you don't know anything about. You proceed estimating the B,C pdfs.

#### tsukiko

##### New Member
Yup, that's what i mean

Yup, yup, that's what i'm doing now. But, i just dont know how to get the initial starting value for the parameters.

Should i simply equate both sample and population moment for both dist B and C respectively and proceed as usual? And forget dist A completely? Sorry for asking so many questions, i'm just too confused now.

#### tsukiko

##### New Member
Thank you..And thank you.

Thank you so much for your help and your quick reply. I gain some confidence in proceeding my work.. Thanks again :tup: