I am trying to build a movement class for a simulated annealing algorithm for predicting an optimal spare parts policy. For better or worse I am looking to the Weibull distribution to move about the high dimensional space using a distribution that is scaled by the periodic demand with a shape parameter to be selected by the user but I want the mode of the distribution to always be centered at zero.
I have tried setting the location parameter equal to the negative of the mode but that was absolutely not what I was looking for. I am 99% certain that this problem needs the use of DIFF EQ which I am trying to brush up on but thought I would throw this out there as a shot in the dark. What I need is a function of $\mu$:
$$ f(x,\gamma,\mu,\alpha)=i\frac{\gamma}{\alpha}(\frac{x-\mu}{\alpha})^{(\gamma-a)}\exp(-(\frac{x-\mu}{\alpha})^\gamma) $$
Where $\gamma$ and $\alpha$ are given (shape parameter and scale parameter respectively), $i\in\{-1$ if $a<0$, 1 otherwise$\}$ and $\mu$ is the location parameter that is variable such that $\max(f(x,\gamma,\mu,\alpha))$ occurs at $x=0$ . As a note, $i$ exists to ensure that my target PDF is always positive regardless of where it occurs on the X-axis, so if this gums up the process, I can always drop it and re-implement the "rule" later.
