Question

2. Consider the density given by gy (y; a, B) -exp the MLEs for α and β assuming both are unknown. the andsity given I"(y re unna expe?) where , 2 Sand.. Find where y 2 B and a > 0. Find Cl

Answer 1

Using log-likelihood method we find out the Maximum likelihood estimators (MLE's):

If we took second derivative to equation 1 with respective to $\alpha$ , we get this derivative is less than zero. Hence $\hat{\alpha}$ is the MLE of parameter $\alpha$ .

Thus $\hat{\alpha}$ and $\hat{\beta}$ are the MLE's of for $\alpha$ and $\beta$.