How to show mathematically max of uniform is a sufficient statistic?

Barrett Osborn

Barrett Osborn

Answered question

2022-11-05

How to show mathematically max of uniform is a sufficient statistic?

Answer & Explanation

Houston Ochoa

Houston Ochoa

Beginner2022-11-06Added 19 answers

Show that the sample mean and variance are sufficient statistics for μ and σ 2 in the case of IID random variables with Normal ( μ , σ 2 ) distributions, where both μ and σ 2 are unknown.
It turns out that a useful "trick" in this area of mathematics is to define h ( x n ) = 1. And so you can use the Fisher-Neyman factorisation theorem to show that the the statistic T(Xn)=max{X1,...,Xn} is sufficient.

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