It is pointed out that in many one-sided testing situations for a real-valued parameter 6, the monotonicity of the power function hinges on the stochastic order of the underlying family of distributions [Fθ] rather than on the stronger property of monotone likelihood ratio of the family. An elementary proof, accessible to students of introductory probability and statistics, is presented.
- Distributions with given marginals
- Power function
- Stochastic order
- Sums of independent random variables