How could one show, that sample circular mean direction $\bar{\theta}$ is unbiased estimate of (theoretical) circular mean direction $\mu$ ?
Even more, i was looking for precise definition of biased/unbiased estimates of circular parameters but failed to found even one. A lot´s of book just say that this one is unbiased estimate of this and that´s all, without any proper defition. So i was wondering if someone could give me clue how to define it?
Thanks for any help. Good day.
The usual distribution on the circle is the Von-Mises Distribution, and if you go to this section they discuss some estimators for the radius and mean along the circle.
The article mostly discusses things as if the circle is defined on the complex plane, but you can map that back to the real plane fairly easily. They talk a little bit about that in the section on the moments.