# Interpretation of confidence intervals for population data?

Suppose that I have access to the observations from the entire population $$x_1,...,x_N$$. If I fit a distribution to this population $$x_i\sim F(\cdot ; \theta)$$, and I calculate confidence intervals/regions for $$\theta$$,

• what is the interpretation of these intervals/regions?
• Haven't I already obtained the true value of the parameter as there are no more individuals?

Even if you can compute the confidence interval in usual manner, those interval are senseless. The usual story behind the confidence interval rules suppose that you collect a sample by $$iid$$ sampling on infinite large population. For finite population some ad hoc adjustments exist (read here: http://www.utstat.toronto.edu/~brunner/oldclass/utm218s07/FinitePop.pdf). From those adjustments you can understand/remember that "confidence interval" regard the inference from sample to population. If you have data at population level the estimators are no more random variables; then no standard deviation exist and, therefore, no confidence intervals.