Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods

Lyman, GJ (2003) Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods. International Journal of Rock Mechanics And Mining Sciences, 40 6: 825-832. doi:10.1016/S1365-1609(03)00043-1


Author Lyman, GJ
Title Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods
Journal name International Journal of Rock Mechanics And Mining Sciences   Check publisher's open access policy
ISSN 1365-1609
Publication date 2003-01-01
Sub-type Article (original research)
DOI 10.1016/S1365-1609(03)00043-1
Volume 40
Issue 6
Start page 825
End page 832
Total pages 8
Editor J.A. Hudson
Place of publication Netherlands
Publisher Elsevier Sc. Ltd.
Language eng
Subject C1
290704 Geomechanics
640200 Primary Mining and Extraction Processes
Abstract There has been a resurgence of interest in the mean trace length estimator of Pahl for window sampling of traces. The estimator has been dealt with by Mauldon and Zhang and Einstein in recent publications. The estimator is a very useful one in that it is non-parametric. However, despite some discussion regarding the statistical distribution of the estimator, none of the recent works or the original work by Pahl provide a rigorous basis for the determination a confidence interval for the estimator or a confidence region for the estimator and the corresponding estimator of trace spatial intensity in the sampling window. This paper shows, by consideration of a simplified version of the problem but without loss of generality, that the estimator is in fact the maximum likelihood estimator (MLE) and that it can be considered essentially unbiased. As the MLE, it possesses the least variance of all estimators and confidence intervals or regions should therefore be available through application of classical ML theory. It is shown that valid confidence intervals can in fact be determined. The results of the work and the calculations of the confidence intervals are illustrated by example. (C) 2003 Elsevier Science Ltd. All rights reserved.
Keyword Engineering, Geological
Mining & Mineral Processing
Rock Mechanics
Discontinuity
Mean Trace Length
Maximum Likelihood
Confidence Interval
Rock Joints
Window Mapping
Discontinuities
Density
Q-Index Code C1

 
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Created: Wed, 15 Aug 2007, 11:18:53 EST