Minitab uses a modified Newton-Raphson algorithm to estimate the model parameters. If you like, you can enter historical estimates for these parameters. In this case, no estimation is done; all results - such as the percentiles - are based on these historical estimates.
When you let Minitab estimate the parameters from the data, you can optionally:
Why enter starting values for the algorithm? The maximum likelihood solution may not converge if the starting estimates are not in the neighborhood of the true solution, so you may want to specify what you think are good starting values for parameter estimates.