The upper quartile of a distribution with cumulative

Chapter , Problem 15

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The upper quartile of a distribution with cumulative distribution F is that point \(q_{.25}\) such that \(F\left(q_{.25}\right)=.75\). For a gamma distribution, the upper quartile depends on \(\alpha\) and \(\lambda\), so denote it as \(q(\alpha, \lambda)\). If a gamma distribution is fit to data as in Example C of Section 8.5 and the parameters \(\alpha\) and \(\lambda\) are estimated by \(\hat{\alpha}\) and \(\hat{\lambda}\), the upper quartile could then be estimated by \(\hat{q}=q(\hat{\alpha}, \hat{\lambda})\). Explain how to use the bootstrap to estimate the standard error of \(\hat{q}\).