Which is an exponential family with sufficient statistic .

For some parametric families, a complete sufficient statistic does not exist.

Also, a minimal sufficient statistic need not exist.

Under mild conditions, a minimal sufficient statistic does always exist.

Fisher required the existence of a sufficient statistic for the fiducial method to apply.

Suppose there is a single sufficient statistic for a single parameter.

The maximum, X, of the n observations is a sufficient statistic for ω.

This expression does not depend on and thus is a sufficient statistic.

A case in which there is no minimal sufficient statistic was shown by Bahadur, 1954.

However, under mild conditions, a minimal sufficient statistic does always exist.