To simplify the process of cost estimation in many engineering applications, deterministic cost models are often used. Single value cost estimates are invariably the output of these models. It has been recognized by the cost estimating community that estimates should more appropriately be given in terms of probability distribution functions (PDFs) and that simulation methods are superior to analytical methods for determining these cost distributions. In this paper, a simulation approach employing non-parametric estimation techniques and their asymptotic properties in the development of the PDFs of cost estimates is proposed. To illustrate the approach, it is applied to the problem of project bidding.