# Tagged Questions

In statistics a pivot, or pivotal quantity is a function of unknown parameters and data whose distribution doesn't depend on the values of the unknown parameters - used to construct confidence intervals.

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### Does pivoting a discrete CDF provide a pivot?

In Section 9.2.3 of Casella's Statistical Inference, they base their confidence interval construction for a parameter $\theta$ on a real-valued statistic $T$ with cdf $F_T(t| \theta)$. They first ...
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### Can pivot be used for testing

A pivotal quantity $Q(X, \theta)$ can be used to construct a confidence interval. I was wondering if it can be used to construct a test statistic and rejection region? In simpler cases involving a ...
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### pivotal statistic versus distribution free statistic

I was wondering what relations and differences are between pivotal statistic versus distribution free statistic? From Wikipedia a pivotal quantity or pivot is a function of observations and ...
I have the following problem: Suppose we have a sample $Y_1,...,Y_n \sim N(\mu, \sigma^2)$. Find the pivotal function for $\sigma^2$ when $\mu$ is known and when $\mu$ is unknown. I know ...