Definition:Simple Hypothesis

Definition

Let $\theta$ be a population parameter of some population.

Let the parameter space of $\theta$ be $\Omega$.

Let $\Omega_0$ and $\Omega_1$ be disjoint subsets of $\Omega$ such that $\Omega_0 \cup \Omega_1 = \Omega$.

Consider the hypotheses:

$H_0: \theta \in \Omega_0$

$H_1: \theta \in \Omega_1$

We call $H_i$, for $i \in \set {0, 1}$, a simple hypothesis if and only if $\Omega_i$ contains only a single element.

Work In Progress In particular: The definition given in Nelson differs from this You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by completing it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{WIP}} from the code.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): simple hypothesis
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): simple hypothesis
• 2011: Morris H. DeGroot and Mark J. Schervish: Probability and Statistics (4th ed.): $9.1$: Problems of Testing Hypotheses: Definition $9.1.2$