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The third quantile of a distribution function F is the point q such that F(q) = 0.75. Note the q (α; λ) (Gamma distribution). Then, the quantile would be estimated by ^q = q (^α; ^λ).

We do have a sample with n=20 from a Gamma distribution:

4.69 0.71 0.52 0.74 0.65 0.08 0.32 0.48 1.22 3.21 1.77 0.61 1.66 0.71 0.65 0.14 0.26 0.65 1.38 0.58

Calculate the estimator ^q and evaluate its standard deviation by the parametric bootstrap method.

Using R, I calculated the sample mean, sample variance then I already found the ^α; ^λ by the method of moments. But then, I don't know how to continue with the estimator ^q..

Please help me to find out! Thank you

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  • $\begingroup$ Welcome to MSE. Please edit and use MathJax to properly format math expressions. $\endgroup$ – Lee David Chung Lin Feb 10 at 6:38

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