A Comparison of Mean Estimators
Date
2014-01-31
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Abstract
The mean values of reservoir parameters such as permeability, porosity, and hydrocarbon reserves are widely used to evaluate a formation for potential development and perform reservoir simulations. Among different mean estimators, the arithmetic average and Swanson’s rule are commonly used within the petroleum industry.
In the petroleum literature, Swanson’s rule has been promoted as a superior alternative to the arithmetic average. A few researchers have evaluated its performance for the case of a log-normal distribution with a limited range of variability but they have overlooked its performance for other types of distribution, which may describe the distributions of reservoir parameters. Prior studies only concentrated on evaluating the bias of Swanson’s rule whereas an optimum mean estimator should simultaneously have zero bias, small uncertainty, consistency, and high efficiency. In addition to bias, this research study, thus, evaluates the performance of mean estimators based on these toher properties.
This research study also compares the performance of Swanson’s rule with some well-known mean estimators: the arithmetic average, maximum likelihood estimator, and Pearson-Tukey’s rule for log normal and the power-normal and bimodal distributions. The mean estimators’ properties are analytically derived and numerically validated via Monte Carlo simulation. We find that none of these mean estimators simultaneously satisfies all conditions of an optimum mean estimator for all ranges of variability and sample size. In other words, each mean estimator can be an optimum mean estimator depending on sample size, variability, and distribution type.
Being unbiased is a desirable property, but it is not necessarily the most important property because a mean estimator can be de-biased. We propose a de-biased version of Swanson’s rule and find it is an appropriate alternative for approximating the mean value, particularly for a data set with large standard deviation and small sample size. Moreover, we evaluate the performance of the mean estimators when data follow a first-order auto-regressive model to illustrate that the auto-correlation causes the mean estimators to behave differently compared to the uncorrelated case.
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Statistics, Engineering--Mining, Engineering--Petroleum
Citation
Moghadasi, M. (2014). A Comparison of Mean Estimators (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/24672