Use equation (17.2) to establish the following distributional relationships that are helpful for calculating quantiles.

a. Assume that \(y_{0}=\alpha_{1} F / \alpha_{2}\), where \(F\) has an \(F\)-distribution with numerator and denominator degrees of freedom \(d f_{1}=2 \alpha_{1}\) and \(d f_{2}=2 \alpha_{2}\). Show that \(y\) has a GB2 distribution.

b. Assume that \(y_{0}=B /(1-B)\), where \(B\) has a beta distribution with parameters \(\alpha_{1}\) and \(\alpha_{2}\). Show that \(y\) has a GB2 distribution.

c. Describe how to use parts (a) and (b) for calculating quantiles.

d. Describe how to use parts (a) and (b) for simulation.

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In y In yo. (17.2)