By extraction of energy resources (oil and gas), we expect the extractive resource is always be decrease over time. But study by authors shows, because of random exploration in the specific time, we have increased in the levels of extractable resources. We indicated (using non-parametric random RUNS test) that change in the level of resources follows a random process at 95 percent significant. In this study we considered sixteen random distributions for this stochastic process in three different models. According to criteria of best Estimation and prediction, hyper geometric and normal distribution is confirmed for this stochastic process as the random distribution of resources. According to the best estimations for extractive resources from 2015 to 2031 the averaging growth rate is predicted -0.4 percent per year. While, average annual growth rate of extractive resources have been 3.1 percent between years 1980 to 2014. According to the forecast, the growth rate for the years of this study (2015-2031) is negative, so the stock of resource will not increase over time. Result of the best model is considered before 2023 the stocks of extractive resources are increasing, but after 2023 the level of resources that can be extracted will be decreasing.