# Mathematical Statistics Lesson of the Day – An Example of An Ancillary Statistic

June 25, 2015 3 Comments

Consider 2 random variables, and , from the normal distribution , where is unknown. Then the statistic

has the distribution

.

The distribution of does not depend on , so is an ancillary statistic for .

Note that, if is unknown, then is not ancillary for .

Will you be giving any examples on real life applications using ancillary statistics? Also, how are you able to write the notation you are using? (I’m curious for my own writing)

Hi Mitchell,

1) I don’t know of real-life applications of ancillary statistics, so I don’t plan on writing about them. The combination of sufficient statistics and ancillary statistics are helpful to understand complete statistics, and that is my goal for talking about them.

2) This particular theme of WordPress (The Enterprise Theme) allows me to write LaTeX in my blog posts. If you want to use WordPress.com to write a blog, choose your theme carefully – not all themes allow LaTeX.

I understand! Thanks and keep writing!