<p>The process of measuring a continuous variable is typically subject to imprecision due to causes as varied as measurement errors or rounding, and it is the duty of practitioners to take account of this imprecision when performing different statistical inference tasks. In this paper, we address the problem of accounting for this imprecision in the context of confidence intervals for parameters of probability distributions. For such purpose, we formalize the notions of inner and outer confidence interval, both of which generalize the classical notion of confidence interval in the presence of imprecision. Different properties of both mathematical constructs are here studied and their explicit expressions are provided in five prominent cases in the field of Statistics.</p>