Here is a result that allows for easy identification of a minimal sufficient statistic: Suppose there is a function t(x₁, …, x_n) such that for any two sets of observations 

a. Identify a minimal sufficient statistic when the X_i’s are a random sample from a Poisson distribution.
b. Identify a minimal sufficient statistic or jointly minimal sufficient statistics when the X_i’s are a random sample from a normal distribution with mean h and variance θ.
c. Identify a minimal sufficient statistic or jointly minimal sufficient statistics when the X_i’s are a random sample from a normal distribution with mean h and standard deviation θ.

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X₁, ..., Xn and y₁, ..., yn, the likelihood ratio f(x1, Xn; 0)/f(v1, Yn: 0) doesn't depend on 0 if and only if t(x₁, t(y₁, yn). Then T = t(X₁, minimal sufficient statistic. The .... .... Xn) = Xn) is a result is also valid if 0 is replaced by 0₁, Om, in which case there will typically be several jointly minimal sufficient statistics. For example, if the underlying pdf is exponen- tial with parameter 2, then the likelihood ratio isx-y, which will not depend on 2 if and only if Σ x = 2 y, so T = = Σ .x; is a minimal sufficient statistic for 2 (and so is the sample mean). .... .... ...