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Given a random variable $X$ which arise from a parameterized distribution $F(X;θ)$, the likelihood is defined as proportional to the probability of observed data as a function of $θ$: $\operatorname{L}(θ | x)=\operatorname{P}(X=x \mid θ)$
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AIC, likelihood, loglikelihood confusion
So are the likelihood values. Are the log-likelihood values positive or negative? … [1] 90785.92
> fit1$AIC
[1] 90909.47
> fit2$AIC
[1] 90839.92
# AIC from likelihood, par1 refers to number of fitted parameters
> 2*par1-2*log(fit1$likelihood)
[1] -14.8344
> 2*par2-2*log(fit2$likelihood …
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AIC and likelihood statistics from tbats (forecast-package in R)
> fit1$likelihood
[1] 90854.67
> fit1$AIC
[1] 90884.67
> par1 # par1 <- length(fit1$parameters$vect), number of fitted parameters
[1] 4
> 2*par1-2*log(fit1$likelihood) # AIC
[1] -14.83403
> fit2$likelihood … But, the likelihood for fit1 is bigger than for fit2. What should I believe? …