I am working with predictive models for wind speeds, which have been given as Gumbel distributions. I need to convert the wind speeds to wind pressures using the formula:
$Pressure = Density * Velocity^2$
So my question is how do I determine the distribution parameters for the wind pressure given the distribution of the velocity?
Also, can I assume that $X^2$ also has a Gumbel distribution? The problem is fairly easy if I can just assume that it has a normal distribution and that:
$E(X^2) = \mu^2 + \sigma^2$
$var(X^2) = E(X^4)-(E(X^2))^2$