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