I am given a dataset generated from the following distribution:
$f(y|\alpha,\beta)=\alpha*\beta^{\alpha}*y^{-(\alpha+1)}$ for $y\geq \beta$
The assumption is that $\beta=2$. The dataset has 8 data which gives a mean of $2.765$. Now,I need to use parametric bootstrap method to generate new datasets, and replicate the process for $1,000$ times. That is, to generate $1,000$ datasets where each of them has $8$ observations based on the distribution with estimated $\alpha=2.765$ and given $\beta=2$.
However, I don't have any idea on how to replicate a sample where the distribution is not a built-in distribution. I searched for several posts and found that it might can be done using functions regarding uniform distribution, but I'm still confused on how to replicate this process.
The cumulative distribution function of $F(y)$ is $F(y)=1-({\beta}/y)^{\alpha}$ if that helps.
Any help will be appreciated.
