In article <[EMAIL PROTECTED]>, Steve Querido <[EMAIL PROTECTED]> wrote: >I'm trying to understand how maximum likelihood is used to obtain >estimates of continuous distributions. My problem is that the >probability that a random variable from a continuous distribution >takes on a point value is 0.
>I understand that the likelihood function is the probabilty that my >data take on their particular values: >L = P(X1 = x1) * P(X2 = x2) * ... * P(Xn = xn) >But doesn't P(X1 = x1) = P(X2 = x2) = 0 if the distribution is >continuous? >How/Why does this work? The likelihood function is not the probability, but is essentially the ratio of the "probability density" to some base measure. This covers both the discrete and the absolutely continuous cases, and more. Multiplying the likelihood function by any function of the state of nature which is finite and non-zero does not change the inference problem at all. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Deptartment of Statistics, Purdue University [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
