What detection thresholds relative to mean noise are required to achieve Pfa 's of 10^-3 and 10^-6 for a Weibull distribution with a mean of 0 dB, assuming a shape parameter of 0.5. Does the log- normal or Weibull distribution require higher detection thresholds for the same characteristics?

Notes:

I believe you can use the icdf function on MATLAB but in doing so, would have to solve for the scale parameter first.

For the log-normal distribution, logninv on MATLAB is also a viable function with mean of 0 dB and stand dev of 9 dB, but the resulting values for 1-Pfa are way too big. Maybe there's a step I'm missing in solving for the log-normal threshold?