Finding Wind Speed using Monte Carlo Simulation or by reverse engineering Weibull Distribution

Question

I have a Weibull distribution that is fit to a set of wind speed data.

Now I want to know if I can use any method to derive the wind speed samples back. I understand there can be an infinite number of results that would be a fit to the Weibull parameters in question but I have heard that Monte Carlo Simulation can be used but am not sure if this is possible.

If anyone here knows please help me with some advice and links that can get me started.

Thank you.

Answer 1

Okay found the answer in this link.

Weibull Distribution Randon variate is given by:

W = α ( − ln (1-R) )^ ( 1 / β )

Where R is the Weibull probability function.

Answer 2

As I understand it, you are looking to generate random variates following the Weibull distribution fitted to the data. This is relatively easy; if the scale parameter is $\alpha$, the shape parameter is $\beta$ and $U$ is uniformly distributed on $[0,1]$, a Weibull random variate is given by the following formula extracted straight from CPython's code: $$W=\alpha(-\log U)^{1/\beta}$$ From the footer of the chart provided, $\alpha=5.50$ and $\beta=2.67$, so you can plug those numbers in and generate variates as you wish.