Chapter 7.4, Problem 53E

a.

To determine

Obtain a likelihood function based on a random sample of size n.

Obtain log likelihood.

b.

To determine

Show that the log likelihood is maximized by the solving the equations

$\beta =\left[\frac{{\displaystyle \sum _{i=1}^n{x}_i^{\beta }\ln \left(x_i\right)}}{{\displaystyle \sum _{i=1}^n{x}_i^{\beta }}}-\frac{{\displaystyle \sum _{i=1}^n\ln \left(x_i\right)}}{n}\right]$, $\delta ={\left[\frac{{\displaystyle \sum _{i=1}^n{x}_i^{\beta }}}{n}\right]}^{1/\beta }$

c.

To determine

Explain the complications that are involved on solving the two equations in part (b).