Some consequences of applying lognormal theory to pseudolognormal distributions

  • Richard F. Link
  • George S. KochJr.


A logarithmic transformation may be used to improve the efficiency of estimates of the mean when observations follow the lognormal distribution. But if this transformation is applied to observations that follow another distribution, bias may be introduced. We consider some consequences of erroneously applying lognormal estimation theory and demonstrate that biased estimates may be obtained for certain classes of distributions. Illustrations of bias obtained in gold sampling are given.

Key words

data processing lognormal theory sampling simulation statistics transformations economic geology mining sedimentology 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Hastings, C., Mosteller, F., Tukey, J. W., and Winsor, C. P., 1947, Low moments for small samples: a comparative study of order statistics: Ann. Math. Stat., v. 18, p. 413–426.Google Scholar
  2. Koch, G. S., Jr., and Link, R. F., 1970, Statistical analysis of geological data, v. 1: John Wiley & Sons, New York, 375 p.Google Scholar
  3. Koch, G. S., Jr., and Link, R. F., 1971, Statistical analysis of geological data, v. 2: John Wiley & Sons, New York, 438 p.Google Scholar
  4. Koch, G. S., Jr., Link, R. F., and Schuenemeyer, J. H., 1972, Computer programs for geology: Artronic Information Systems, Inc., New York, 142 p.Google Scholar
  5. Krige, D. G., 1952, A statistical analysis of some of the borehole values in the Orange Free State goldfield: Jour. Chem. Met. and Min. Soc. of South Africa, v. 53, p. 47–70.Google Scholar
  6. Krige, D. G., 1960, On the departure of ore value distributions from the lognormal model in South African gold mines: Jour. South African Inst. Mining Metall., v. 61, no. 4, p. 231–244.Google Scholar
  7. Link, R. F., Koch, G. S., Jr., and Schuenemeyer, J. H., 1971, Statistical analysis of gold assay and other trace element data: U.S. Bur. Mines Rept. Invest. 7495, 127 p.Google Scholar
  8. Sarma, D. D., 1969, A preliminary statistical study on the basic mine valuation problems at Kolar goldfields, Mysore state (India): Geoexploration, v. 7, no. 2, p. 97–105.Google Scholar
  9. Sarma, D. D., 1970, A statistical study in mining exploration as related to the Kolar gold fields (India): Geoexploration, v. 8, no. 1, p. 19–35.Google Scholar
  10. Sichel, H. S., 1947, An experimental and theoretical investigation of bias error in mine sampling with special reference to narrow gold reefs: Trans. Inst. Min. and Met. (London), v. 56, p. 403–474.Google Scholar

Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • Richard F. Link
    • 1
  • George S. KochJr.
    • 2
  1. 1.Artronic Information SystemsNew YorkUSA
  2. 2.Department of GeologyUniversity of GeorgiaUSA

Personalised recommendations