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Original Articles

Maximum Likelihood Estimation Under a Successive Sampling Discovery Model

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Pages 423-436 | Published online: 23 Mar 2012

REFERENCES

  • Andreatta , G. and Kaufman , G. M. 1986 . “Estimation of Finite Population Properties When Sampling Is Without Replacement and Proportional to Magnitude,” . Journal of the American Statistical Association , 81 : 657 – 666 .
  • Arps , J. J. and Roberts , T. G. 1958 . “Economics of Drilling for Cretaceous Oil Production on the East Flank of the Denver-Julesberg Basin,” . Bulletin of the American Association of Petroleum Geologists , 42 : 2549 – 2566 .
  • Barouch , E. and Kaufman , G. M. 1976 . “Probabilistic Modelling of Oil and Gas Discovery,”. ” . In Energy: Mathematics and Models Edited by: Roberts , F. 248 – 260 . Philadelphia : Society for Industrial and Applied Mathematics. .
  • Barouch , E. and Kaufman , G. M. “Estimation of Undiscovered Oil and Gas,” . Proceedings of Symposium in Applied Mathematics . Vol. 21 , pp. 77 – 91 . Providence , RI : American Mathematical Society. .
  • Barouch , E. , Kaufman , G. M. and Nelligan , J. 1983 . “Estimation of Parameters of Oil and Gas Discovery Process Models Using the Expectation-Maximization Algorithm,”. ” . In Energy Modelling and Simulation Edited by: Kydes , A. S. 109 – 117 . Amsterdam : North-Holland. .
  • Bickel , P. J. , Nair , V. N. and Wang , P. C. C. 1989 . “Non-parametric Inference Under an Informative Sampling Design,” unpublished manuscript
  • Bloomfield , P. , Deffeyes , K. S. , Watson , G. S. , Benjamini , Y. and Stine , R. A. 1979 . “Volume and Area of Oil Fields and Their Impact on Order of Discovery,” Princeton University, Depts. of Statistics and Geology. . Report of the Resource Estimation and Validation Project
  • Cleveland , W. S. 1979 . “Robust Locally Weighted Regression and Smoothing Scatterplots,” . Journal of the American Statistical Association , 74 : 829 – 836 .
  • Cox , D. R. 1969 . “Some Sampling Problems in Technology,”. ” . In New Developments in Survey Sampling Edited by: Johnson , N. L. and Smith , H. Jr. 506 – 527 . New York : Wiley-Interscience. .
  • Cox , D. R. and Hinkley , D. V. 1974 . Theoretical Statistics New York : Chapman & Hall. .
  • Cozzolino , J. M. 1972 . “Sequential Search for an Unknown Number of Objects of Nonuniform Size,” . Operations Research , 20 : 293 – 308 .
  • Crump , K. S. 1976 . “Numerical Inversion of Laplace Transforms Using a Fourier Series Approximation,” . Journal of the Association for Computing Machinery , 23 : 89 – 96 .
  • Davies , R. B. 1980 . “The Distribution of a Linear Combination of x2 Random Variables,” . Applied Statistics , 29 : 323 – 333 .
  • Dempster , A. P. , Laird , N. M. and Rubin , D. B. 1977 . “Maximum Likelihood From Incomplete Data Via the E-M Algorithm,” . Journal of the Royal Statistical Society , 39 : 1 – 39 . Ser. B
  • Energy Resources Conservation Board . 1985 . Alberta's Reserves of Crude Oil, Oil Sands, Gas, Natural Gas Liquids, and Sulphur Calgary , , Alberta : Author. .
  • Gordon , L. 1983 . “Estimation for Large Successive Samples With Unknown Inclusion Probabilities,” unpublished manuscript
  • IMSL . 1984 . IMSL User's Manual, , Edition 9.2 Vol. 2 , Houston : International Mathematical and Statistical Libraries. .
  • Johnson , N. L. and Kotz , S. 1970 . Continuous Univariate Distributions—1 Boston : Houghton Mifflin. .
  • Kaufman , G. , Balcer , Y. and Kruyt , D. 1975 . “A Probabilistic Model of Oil and Gas Discovery,”. ” . In Estimating the Volume of Undiscovered Oil and Gas Resources Edited by: Haun , J. 113 – 142 . Tulsa , OK : American Association of Petroleum Geologists. .
  • Lee , P. J. and Wang , P. C. C. 1985 . “Prediction of Oil or Gas Pool: Sizes When Discovery Record Is Available,” . Journal of the International Association of Mathematical Geology , 17 : 95 – 113 .
  • Lee , P. J. and Wang , P. C. C. 1986 . “Evaluation of Petroleum Resources From Pool Size Distributions,”. ” . In Oil and Gas Assessment—Methods and Applications (Studies in Geology, No. 21) Edited by: Rice , D. D. 33 – 42 . Tulsa , OK : American Association of Petroleum Geologists. .
  • Littlewood , B. 1981 . “Stochastic Reliability-Growth: A Model for Fault-Removal in Computer-Programs and Hardware-Designs,” . IEEE Transactions of Reliability , 30 : 313 – 320 .
  • Mallows , C. L. and Nair , V. N. 1987 . “A Unique Unbiased Estimator With an Interesting Property,” . The American Statistician , 41 : 205 – 206 .
  • Patil , G. P. and Rao , C. R. 1977 . “The Weighted Distributions: A Survey of Their Applications,”. ” . In Application of Statistics Edited by: Krishnaiah , P. R. 383 – 405 . Amsterdam : North-Holland. .
  • Patil , G. P. and Rao , C. R. 1978 . “Weighted Distributions and Size-Biased Sampling With Applications to Wildlife Populations and Human Families,” . Biometrics , 34 : 179 – 189 .
  • Scheaffer , R. L. 1972 . “Size-Biased Sampling,” . Technometrics , 14 : 635 – 644 .
  • Sheil , J. and O'Muircheartaigh , I. 1977 . “The Distribution of Non-negative Quadratic Forms in Normal Variables,” . Applied Statistics , 26 : 92 – 98 .
  • Smith , J. L. and Ward , G. L. 1981 . “Maximum Likelihood Estimates of the Size Distribution of North Sea Oil Fields,” . Journal of the International Association of Mathematical Geology , 13 : 399 – 413 .
  • Stoakes , F. 1980 . “Nature and Control of Shale Basin Fill and Its Effect on Reef Growth and Termination: Upper Devonian Duvernay and Ireton Formations of Alberta, Canada,” . Bulletin of Canadian Petroleum Geology , 28 : 345 – 410 .
  • Vardi , Y. 1982 . “Nonparametric Estimation in the Presence of Length Bias,” . The Annals of Statistics , 10 : 616 – 620 .
  • Wang , P. C. C. and Nair , V. N. 1988 . “Statistical Analysis of Oil and Gas Discovery Data,”. ” . In Quantitative Analysis of Mineral and Energy Resources (NATO ASI series) Edited by: Chung , C. E , Fabbri , A. G. and Sinding-Larsen , R. 199 – 214 . Boston : D. Reidel. .
  • Wu , C. F. J. 1983 . “On the Convergence Properties of the E-M Algorithm,” . The Annals of Statistics , 11 : 95 – 103 .

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