# Tag Info

### limiting the log-likelihood function for Weibull distribution

I believe that the issue is about the sufficiency of the solution to the first order condition with respect to the global optimization problem. As you showed that the log-likelihood function is ...
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• 3,935
1 vote

### Maximum Likelihood and method of moment estimation

The reason you usually differentiate the log likelihood function is that it's typically the easiest way to do what you're really trying to do, which is to maximize the likelihood function. So, let's ...
• 10.2k
Accepted

### Compute the MLE of variance for $f(x) = 3x^3 /\theta^3$

By the invariance property of MLE, if $\widehat{\theta}$ is a MLE of a parameter $\theta$ and $g: \mathbb{R} \to \mathbb{R}$ is a function, then $g(\widehat{\theta})$ is a MLE of $g(\theta)$. Since ...
• 1,624
Accepted

### Maximum Likelihood Estimation on a standardized normal variable

Ignoring the MLE part of the question, the change in density function for a location-scale change is not difficult, though with a normal distribution you have to be careful not to confuse the variance ...
• 145k
1 vote

### Not understanding Maximum Likelihood last steps

The result given in the book is based on a property that is called "functional equivariance". Or functional invariance. See So as you have correctly calculated $\hat{\beta}=1.6225$. Now ...
• 3,218
1 vote
Accepted

### Not understanding Maximum Likelihood last steps

The key insight is that you are not interested in estimating the parameter $\beta$ itself, but rather, a function of that parameter, which the solution calls $h$. Getting an estimate of $\beta$ is ...
• 115k

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