Improved documentation for calculating CV(N_hat)

[LHMarshall]

Copied from an issue in Distance but relates to mrds

[LHMarshall]

Add this in before the last paragraph. Add in heading if possible and change semi colon at end of list at the top to a .

[LHMarshall]

@erex is this all correct? Thanks

#' 
#' The coefficient of variation (CV) associated with the abundance estimates is calculated based on the following formula for the \code{varflag} options 1 and 2:
#' 
#' \code{varflag=1}
#' 
#' \deqn{CV(\hat{N}) = \sqrt{\left(\frac{\sqrt{n}}{n}\right)^2+CV(\hat{p})^2}}
#' 
#' \code{varflag=2}
#' 
#' \deqn{CV(\hat{N}) = \sqrt{\left(\frac{\sqrt{\hat{N}}}{\hat{N}}\right)^2+CV(\hat{p})^2}}
#' where n is the number of observations, \eqn{\hat{N}} is the estimated
#' abundance and \eqn{\hat{p}} is the average probability of detection for
#' an animal in the covered area.

[erex]

yes, those equations are associated with the right varflag option

[LHMarshall]

yes, those equations are associated with the right varflag option

and the text ok too? Is N_hat the estimated abundance or particularly the estimated abundance in the covered area? And the definition for p_hat is correct? Thanks

[erex]

This issue #117 was spawned from another issue (now closed) where these calculations were derived. I've tried to find that closed issue, because I think it would answer your question, but I can't find that closed issue. Do you remember which issue you were using to create #117?

[erex]

I found the issue from which issue #117 was derived; it is closed Distance issue #192. In issue #192, I produced a Quarto document from which the equations you are asking about were derived:

issue192.pdf

That document shows the $\hat{N}$ in question is actual abundance in study area (not covered region). Definition of $\hat{p}$ is as you describe.

[LHMarshall]

Thanks @erex