Slides08-2010 - Outline Empirical Maximum Likelihood Empirical Maximum Likelihood Lecture VIII Charles B Moss Charles B Moss Empirical Maximum

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Unformatted text preview: Outline Empirical Maximum Likelihood Empirical Maximum Likelihood: Lecture VIII Charles B. Moss September 10, 2010 Charles B. Moss Empirical Maximum Likelihood Outline Empirical Maximum Likelihood Empirical Maximum Likelihood Newton-Raphson Example Charles B. Moss Empirical Maximum Likelihood Outline Empirical Maximum Likelihood Newton-Raphson Example Empirical Maximum Likelihood I To demonstrate the estimation of the likelihood functions using maximum likelihood, we formulate the estimation problem for the gamma distribution for the same dataset including a trend line in the mean. I The basic gamma distribution function is L = N Y i =1 1 Γ ( α ) β α x α − 1 exp − x β ⇒ ln ( L ) = N X i =1 − ln (Γ ( α )) − α ln ( β ) + ( α − 1) x i − x i β (1) Charles B. Moss Empirical Maximum Likelihood Outline Empirical Maximum Likelihood Newton-Raphson Example I Next, we add the possibility of a trend line max α ,α 1 ,β ln ( L ) = T X t =1 [ − ln (Γ ( α + α 1 t )) − ( α + α 1 t ) ln ( β ) + ( α + α 1 t − 1) x t − x t β (2) I Given the implicit nonlinearity involved, we will solve for the optimum using the nonlinear optimization techniques.optimum using the nonlinear optimization techniques....
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This note was uploaded on 07/15/2011 for the course AEB 6182 taught by Professor Weldon during the Fall '08 term at University of Florida.

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Slides08-2010 - Outline Empirical Maximum Likelihood Empirical Maximum Likelihood Lecture VIII Charles B Moss Charles B Moss Empirical Maximum

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