Statistics · Maths EE idea · Solid
Estimating the largest serial number
A research question to start from
What is the best way to estimate the total number N from a sample of serial numbers, and how do the estimators compare?
A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.
Why it works as a maths EE
Competing estimators with exact properties you can derive and compare.
Mathematics you would need
- Discrete uniform distribution
- Order statistics
- Unbiased estimators
- Variance comparison
Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.
One possible line of attack
- Propose several estimators (maximum, mean-based, gap-corrected).
- Derive their bias and variance.
- Compare by simulation and explain the winner.
Scope and difficulty
Solid. Solid.
Pitfalls
- History taking over.
- Comparing without a criterion.
Where to start reading
Search a library catalogue or a university's open lecture notes for: German tank problem minimum variance unbiased estimator; order statistics uniform. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).