I got a sample of a distribution that is supposed to be normally distributed in time. Max is reached in <micro> years, not necessaryly an integer.

Question: how do I find the (best, 3) parameters.
Note: For example, for t=0, 1, 2, ... years the values might be:
80, 93, 100, 93, 80, 60, .... with a clear micro of 2 years or
82, 94, 100, 92, 79, 58,... etc.

Thx four your help. The problem seems so simple but I find it hard to get a solution.