Determination of the yet to be produced oil and gas prescribes the assets of a company. This is important internally in regard to budgeting and externally in regard to the valuation of the company. The yet to be produced oil and gas are known as reserves and their determination from historical trends, known as decline curves, are the subject of this thesis. The culmination of this work is to determine stochastic reserves for wells producing in infinite acting linear-flow based on statistical sampling of mature wells whose production life has extended into mature flow-regimes.