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Corrigendum to “Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods”
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International Journal of Rock Mechanics & Mining Sciences 41 (2004) 1053
Corrigendum
Corrigendum to ‘‘Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods’’ [International Journal of Rock Mechanics and Mining sciences 40 (2003) 825–832]$ G.J. Lyman* Julius Kruttschnitt Mineral Research Centre, University of Queensland, Isles Road, Indooroopilly, Queensland 4068, Australia Accepted 13 April 2004
The author’s paper [1] dealt with the non-parametric estimation of mean trace length for window-mapped data. It was demonstrated that the problem could be cast as a formal maximum likelihood (ML) problem. The theory behind ML estimation problems provides an asymptotic result for the joint distribution of the estimated parameter values which applies in the case of a ‘large’ data set. In any ML solution to a parameter estimation problem, the determination of how large the data set must be for the asymptotic result to hold true is a matter of practical importance. The work demonstrated that the asymptotic result was valid even with quite small numbers of logged traces. In the setting out of the theory to be used for the confidence interval calculation, two typographical errors went undetected.
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doi of original article 10.1016/S1365-1609(03)00043-1 *Tel.: +61-7-3365-5888; fax: +61-7-3365-5999. E-mail address: [email protected] (G.J. Lyman).
1365-1609/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmms.2004.04.002
Eqs. (18) and (20) should involve the inverse of the information matrix M as follows. " # * iÞ Lðyjx # # T M1 ðy* yÞ 2ln ¼ ðy* yÞ # iÞ Lðyjx ¼ 2R " # Lðy# 0 jx0 Þ # T M1 ðy# 0 yÞ # 2ln ¼ ðy# 0 yÞ # 0Þ Lðyjx
ð18Þ ð20Þ
References [1] Lyman GJ. Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods. Int J Rock Mech Min Sci 2003;40:825–32.
International Journal of Rock Mechanics & Mining Sciences 41 (2004) 1053
Corrigendum
Corrigendum to ‘‘Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods’’ [International Journal of Rock Mechanics and Mining sciences 40 (2003) 825–832]$ G.J. Lyman* Julius Kruttschnitt Mineral Research Centre, University of Queensland, Isles Road, Indooroopilly, Queensland 4068, Australia Accepted 13 April 2004
The author’s paper [1] dealt with the non-parametric estimation of mean trace length for window-mapped data. It was demonstrated that the problem could be cast as a formal maximum likelihood (ML) problem. The theory behind ML estimation problems provides an asymptotic result for the joint distribution of the estimated parameter values which applies in the case of a ‘large’ data set. In any ML solution to a parameter estimation problem, the determination of how large the data set must be for the asymptotic result to hold true is a matter of practical importance. The work demonstrated that the asymptotic result was valid even with quite small numbers of logged traces. In the setting out of the theory to be used for the confidence interval calculation, two typographical errors went undetected.
$
doi of original article 10.1016/S1365-1609(03)00043-1 *Tel.: +61-7-3365-5888; fax: +61-7-3365-5999. E-mail address: [email protected] (G.J. Lyman).
1365-1609/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmms.2004.04.002
Eqs. (18) and (20) should involve the inverse of the information matrix M as follows. " # * iÞ Lðyjx # # T M1 ðy* yÞ 2ln ¼ ðy* yÞ # iÞ Lðyjx ¼ 2R " # Lðy# 0 jx0 Þ # T M1 ðy# 0 yÞ # 2ln ¼ ðy# 0 yÞ # 0Þ Lðyjx
ð18Þ ð20Þ
References [1] Lyman GJ. Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods. Int J Rock Mech Min Sci 2003;40:825–32.