Minimum Sufficient Statistic for Uniform(θ,θ+1) distribution?

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I saw that (min(X), max(X)) are minimal sufficient statistic for this.

But I was wondering, why can't we just have min(X) OR max(X)?

If distribution is Uniform(θ1,θ2), then it makes sense to have two dimensional minimum sufficient statistic, but if not then why can't we recover θ from min(X) OR max(X)?