# Does p-value (significance) function a cumulative distribution function (CDF) for every fixed sample $X$?

by score324   Last Updated October 11, 2018 15:19 PM

Let's consider a one-sided hypothesis test $$H_{0}:\theta \leq \theta_{0}$$ vs $$H_{1}:\theta > \theta_{0}$$, for a given $$\theta_{0}$$ in the parameter space $$\Theta$$. Now the p-value function is,

P - value function $$p_{n} = p_{n}(\theta_{0}) = p_{n}(x,\theta_{0}) = P(T>t|\theta = \theta_{0})$$.

How $$p_{n}(.)$$ is a cumulative distribution function for every fixed sample $$X$$?

(Please see http://www.stat.rutgers.edu/home/mxie/RCPapers/insr.12000.pdf, on page 9 (top -left hand corner) they mentioned that $$p_{n}(.)$$ is a cumulative distribution function).

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