Assessment of the Initial, Promising, and Predicted Geologic and Recoverable Oil Resources of the West Siberian Petroleum Province and Their Structure

—The structure of the initial and predicted oil resources of the West Siberian petroleum province is quantitatively assessed. The assessment is based on the law of mass distribution of hydrocarbon accumulations, i.e., the truncated Pareto distribution and simulation modeling of the general set of oil fields. This approach makes it possible to estimate the amount of oil and the total oil resources concentrated in intervals of any size, in particular, in intervals of small and fine fields, in order to determine the economic efficiency of their development. The considered estimates do not apply to unconventional resources, such as the shale oil of the Bazhenov Formation.

A Weighted Estimation for Risk Model

We propose a weighted estimation method for risk models. Two examples of natural disasters are studied: hurricane loss in the USA and forest fire loss in Canada. Risk data is often fitted by a heavy-tailed distribution, for example, a Pareto distribution, which has many applications in economics, actuarial science, survival analysis, networks, and other stochastic models. There is a difficulty in the inference of the Pareto distribution which has infinite moments in the heavy-tailed case. Firstly this paper applies the truncated Pareto distribution to overcome this difficulty. Secondly, we propose a weighted semiparametric method to estimate the truncated Pareto distribution. The idea of the new method is to place less weight on the extreme data values. This paper gives an exact efficiency function, L1-optimal weights and L2-optimal weights of the new estimator. Monte Carlo simulation results confirm the theoretical conclusions. The two above mentioned examples are analyzed by using the proposed method. This paper shows that the new estimation method is more efficient by mean square error relative to several existing methods and fits risk data well.

A Cluster Truncated Pareto Distribution and Its Applications

The Pareto distribution is a heavy-tailed distribution with many applications in the real world. The tail of the distribution is important, but the threshold of the distribution is difficult to determine in some situations. In this paper we consider two real-world examples with heavy-tailed observations, which leads us to propose a mixture truncated Pareto distribution (MTPD) and study its properties. We construct a cluster truncated Pareto distribution (CTPD) by using a two-point slope technique to estimate the MTPD from a random sample. We apply the MTPD and CTPD to the two examples and compare the proposed method with existing estimation methods. The results of log-log plots and goodness-of-fit tests show that the MTPD and the cluster estimation method produce very good fitting distributions with real-world data.