A aniguchisan May 2010 6 0 May 11, 2010 #1 Hi, I have the following question about Gamma Distributions and Transformations. Given the following: It is easy to work out that the MGF of X is: Now, my doubts lie upon the following. Could someone give me a detailed run through these next two questions? As always, any help is greatly appreciated.

Hi, I have the following question about Gamma Distributions and Transformations. Given the following: It is easy to work out that the MGF of X is: Now, my doubts lie upon the following. Could someone give me a detailed run through these next two questions? As always, any help is greatly appreciated.

Anonymous1 Nov 2009 517 130 Big Red, NY May 11, 2010 #2 aniguchisan said: Hi, I have the following question about Gamma Distributions and Transformations. Given the following: It is easy to work out that the MGF of X is: Now, my doubts lie upon the following. Could someone give me a detailed run through these next two questions? As always, any help is greatly appreciated. Click to expand... (a) Multiplicative principle of MGF says: \(\displaystyle M_Z = M_{X_1}\cdot M_{X_2} = (1-\frac{r}{\beta})^{-\alpha_1}(1-\frac{r}{\beta})^{-\alpha_2} = (1-\frac{r}{\beta})^{-(\alpha_1+\alpha_2)} \) Uniqueness implies: \(\displaystyle Z \sim G\Big((\alpha_1+\alpha_2),\beta\Big)\)

aniguchisan said: Hi, I have the following question about Gamma Distributions and Transformations. Given the following: It is easy to work out that the MGF of X is: Now, my doubts lie upon the following. Could someone give me a detailed run through these next two questions? As always, any help is greatly appreciated. Click to expand... (a) Multiplicative principle of MGF says: \(\displaystyle M_Z = M_{X_1}\cdot M_{X_2} = (1-\frac{r}{\beta})^{-\alpha_1}(1-\frac{r}{\beta})^{-\alpha_2} = (1-\frac{r}{\beta})^{-(\alpha_1+\alpha_2)} \) Uniqueness implies: \(\displaystyle Z \sim G\Big((\alpha_1+\alpha_2),\beta\Big)\)

matheagle MHF Hall of Honor Feb 2009 2,763 1,146 May 11, 2010 #3 I'm not sure what you want. The instructions are quite explicit. This is not a difficult problem and it's been solved here several times.

I'm not sure what you want. The instructions are quite explicit. This is not a difficult problem and it's been solved here several times.

Anonymous1 Nov 2009 517 130 Big Red, NY May 11, 2010 #4 matheagle said: \(\displaystyle \color{red}{\text{Not sure what you want.}}\) \(\displaystyle \color{red}{\text{The guide is quite explicit.}}\) \(\displaystyle \color{red}{\text{This has been solved here.}}\) Click to expand... NOW, it's a Haiku. Reactions: matheagle

matheagle said: \(\displaystyle \color{red}{\text{Not sure what you want.}}\) \(\displaystyle \color{red}{\text{The guide is quite explicit.}}\) \(\displaystyle \color{red}{\text{This has been solved here.}}\) Click to expand... NOW, it's a Haiku.

matheagle MHF Hall of Honor Feb 2009 2,763 1,146 May 11, 2010 #5 if u say so I'm not an expert on poetry