It´s probably basic question, but I am wondering, what is meant by the term "joint observations"? I´ve seen this for the first time, and in the literature (statistical one) I am using, it´s not wisely interpreted. So, does somebody know, the meaning of it?

The sentences, where it ossurs are:

  1. Turning to bivariate data, the natural support for joint observations on two circular random variables is the unit torus; and a cylinder with unit radius for joint observations on one circular random variable and one linear one.

  2. .....joint observations on two circular random variables, and cylindrical data, corresponding to joint observations on one linear random variable and one circular random variable,

I would say, it should be observations, measured somehow jointly, during some time interval?

  • $\begingroup$ Can you edit your post to include more context like the whole sentence in which it occurred? $\endgroup$ – mdewey Nov 24 '17 at 17:07
  • $\begingroup$ ok, sure i will do it. $\endgroup$ – stanly Nov 24 '17 at 17:09
  • $\begingroup$ I added the terminology tag as well. $\endgroup$ – mdewey Nov 24 '17 at 17:31

It means that the two variables were measured jointly. So, for example, if you measured the angle something was travelling at (a circular random variable) and its speed (a linear random variable) those would be joint observations and as your first quote says the support for their distribution would be a cylinder.

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  • $\begingroup$ So basically, it´s measured at the same time (both ''informations"), and to some extent, like one random variable (or basically random vector, with ''different'' components), right? $\endgroup$ – stanly Nov 24 '17 at 17:41
  • $\begingroup$ Yes, that is another way of phrasing it. $\endgroup$ – mdewey Nov 24 '17 at 18:15
  • $\begingroup$ Perfect, thanks a lot for your help. I really appreciate that. $\endgroup$ – stanly Nov 24 '17 at 18:22

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