average of detection probabilities

[Eurycea]

Thank you for your response Cooch. I will work from the whole book, as you suggest.

I have a follow-up question. I have now calculated average parameter estimates using the variance components method for the conditional capture probability, p, and the temporary emigration rate, gamma. I would like to calculate an average effective capture probability and was wondering if I could simply use the equations 5 and 6 from Kendall et al. (1997). Eq 5:

gamma-hat (i)= 1 - [ p-hat(js,i) / p-hat(cl,i) ]

js and cl are superscripts, i is the subscript.

where (roughly) p-hat (js,i) is the effective capture probability from open population model, and p-hat(cl,i) is the conditional capture probability, and gamma-hat is the temporary emigration parameter, all at time i.

The essence of my question is whether I can use an AVERAGE of my time-varying estimates (from the variance components method) to generate an AVERAGE of the estimate I'm interested in. I'm not a mathematician or statistician (if that is not painfully obvious) so I just want to make sure I'm not committing some cardinal sin by substituting averages into an equation where they don't belong. Thanks!

Nathan