{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture20a-2010

# Lecture20a-2010 - Empirical Maximum Likelihood and Method...

This preview shows pages 1–3. Sign up to view the full content.

Empirical Maximum Likelihood and Method of Moment Estimation: Lecture XXa Charles B. Moss October 21, 2010 I. Gamma Distribution Function f ( x | α, β ) = x α 1 exp x β Γ ( α ) β α (1) A. The likelihood function for a sample of random variables dis- tributed gamma can be expressed as L ( x 1 , x 2 , · · · x n | α, β ) = 1 (Γ ( α ) β α ) n n i =1 x α 1 i exp x i β . (2) B. Taking the logarithm of the likelihood function ln ( L ( x 1 , x 2 , · · · x n | α, β )) = n ln (Γ ( α )) ln ( β ) + ( α 1) n i =1 ln ( x i ) 1 β n i =1 x i (3) C. Note that if we define two statistics T 1 = n i =1 ln ( x i ) T 2 = n i =1 x i (4) 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
AEB 6571 Econometric Methods I Professor Charles B. Moss Lecture XXa Fall 2010 The sample likelihood function becomes ln ( L ( x 1 , x 2 , · · · x n | α, β )) = n ln (Γ ( α )) ln ( β ) + ( α 1) T 1 1 β T 2 (5) D. Code to estimate the parameters of the gamma in R is then dta <- read.table("Gamma Data 2007.dta") t1 <- sum(dta) t2 <- sum(log(dta)) fr <- function(b) { nrow(dta)*lgamma(b[1])+nrow(dta)*b[1]*log(b[2]) - (b[1]-1)*t2+1/b[2]*t1 }
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

Lecture20a-2010 - Empirical Maximum Likelihood and Method...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online