Chuntao,
The function -phi- is, as you say, defined for the standard normal. The
relationship between this -phi- and the probability distribution
function for a generalised normal, i.e. where sigma=/=1, is
(1/sigma)phi((y-x*beta)/sigma).
Note that the (1/sigma) comes from the differentiation of the normalised
cumulative density function Phi((y-x*beta)/sigma) with respect to
x*beta.
Take logs, and you're there.
Julian
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Lee Chuntao
Sent: 24 July 2003 06:13
To: [email protected]
Subject: st: Likelihood Function
Dear Listers,
In page 29 of Maximum Likelihood Estimation with Stata (Gould and
Sribney 1999), the likelihood function for the linear regression model
is
written as:
lnL=SUM (ln (phi((y-x*beta)/sigma)) - ln(sigma))
where phi() is the standard normal PDF.
My Question is: How the last term, ln(sigma), comes to the likelihood
function?
Can you knidly give me some ideas?
thanks in advance
Chuntao
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