Confidence intervals (CIs) are common methods to characterize the uncertain output of experimental measurements, process design calculations and simulations. Usually, probability distributions (pdfs) such as Gaussian and t-Student are used to quantify them. There are situations where the pdfs have anomalous behavior such as heavy tails, which can arise in uncertainty analysis of nonlinear computer models with input parameters subject to different sources of errors. We present a method for the estimation of CIs by analyzing the tails of the pdfs regardless of their nature. We present case studies in which heavy tail behavior appears due to the systematic errors in the input variables of the model. Taking into account the probability distributions behavior to estimate appropriate CIs is a more realistic approach to characterize and analyze the effect of random and systematic errors for uncertainty analysis of computer models.