By comparing various distributions and by choosing the one that has the minimal total error. It is an optimization problem. Let's put it as follows. Which optimal estimation regarding a series of known distributions offers minimal total error. So you need. 1. Discrete Optimization skills, 2. Constrained optimization skills for continuous problems.
Knowledge in Differential Calculus (including linear algebra) 4. Knowledge of statistics: distribution of errors, variance analysis, and sample mean and variance estimations 5. Knowledge of Mathematics: partial differential equations, integral calculus, optimization problems, and more. 6. Knowledge of Geometrics: geometry tools (lines, spheres, etc.), construction of graphs, distance estimates, etc. 7. Knowledge of Statistics: random sampling method, inference methods, and more. I hope this was a useful post about estimation of distributions. The rest, I hope, is an eye-opener, especially for beginners. (You can download this book without credit.