Let X1, , Xn be a random sample from a gamma(a, () population a Find the MLE of , assuming is known b If and are both unknown, there is no explicit formula for the MLEs of and , but the maximum can be found numerically The result in part (a) can be used to reduce the problem to the maximization of ...

a Set the partial derivative equal to 0 and solve for to obtain i x i n To check that this is a maxi ...

Let X1,..., Xn be a random sample from a gamma(a, () population. a. Find the MLE of

Question:

Let X1,..., Xn be a random sample from a gamma(a, (β) population.
a. Find the MLE of β, assuming α is known.
b. If α and β are both unknown, there is no explicit formula for the MLEs of α and β, but the maximum can be found numerically. The result in part (a) can be used to reduce the problem to the maximization of a univariate function. Find the MLEs for α and β for the data in Exercise 7.10(c).