Sufficient statistics

• What Is a Sufficient Statistic for the Beta Distribution?
  For an iid Beta(alpha, beta) sample with both shape parameters unknown, the minimal sufficient statistic is the pair of sums of log observations and log complements.
• What Is the Minimal Sufficient Statistic for Uniform(θ, θ)?
  For Uniform(θ, θ), the endpoints coincide, so the model is degenerate; for a nonzero interval, the minimal statistic depends on its endpoints.