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  • 1 Institute of Mathematics and Informatics, Szent István University, Gödöll? H-2103 Gödöll?, Páter Károly u. 1, Hungary
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In this paper we will demonstrate the use and efficiency of the bootstrap on a geologic problem. The tools of classical statistics are often not applicable because they strongly depend on certain conditions that are not fulfilled. Explicit mathematical formulas for standard errors and confidence intervals with respect to a parameter either require some specific (generally normal) distribution, or they do not exist at all. Hypothesis tests may also only be carried out if some conditions are satisfied. Using the bootstrap method one can simulate the unknown distribution of an arbitrary statistic by its bootstrap replicates; hence any characteristics (standard error, confidence intervals, and test significance levels) can be obtained through direct empirical calculations. We applied the bootstrap to the chemical composition data of rock samples from the Boda Claystone Formation, Hungary. First we investigated the distribution of 8 chemical components in a rock sample group of few elements, computing standard errors and confidence intervals for the mean, the standard deviation and the skewness of these distributions. Then two groups of rock samples from different sampling regions were compared using hypothesis tests.  

  • Efron, B. 1981: Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods. - Biometrika, 68, pp. 589-599.

    'Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods. ' () 68 Biometrika : 589 -599.

    • Search Google Scholar
  • Efron, B., R. Tibshirani 1993: An Introduction to the Bootstrap. - Chapman & Hall, New York, London, 436 p.

    An Introduction to the Bootstrap. , () 436.

  • Efron, B. 1987: Better bootstrap confidence intervals. - J. Am. Stat. Assoc, 82, pp. 171-200.

    ': Better bootstrap confidence intervals. ' () 82 J. Am. Stat. Assoc : 171 -200.

  • Kovács, L., G. Hámos, J. Csicsák 2000: Actual state of the site characterisation programme of the Boda Siltstone Formation. - Bulletin of the Hungarian Geological Society, 130, pp. 197-206.

    'Actual state of the site characterisation programme of the Boda Siltstone Formation. ' () 130 Bulletin of the Hungarian Geological Society : 197 -206.

    • Search Google Scholar
  • Caers, J., J. Beirlant, M.A. Maes 1999: Statistics for modeling heavy tailed distributions in geology: Part I. Methodology. - Math. Geology, 31, pp. 391-410.

    Statistics for modeling heavy tailed distributions in geology: Part I. Methodology. Math. Geology , () 31, 391 -410.

    • Search Google Scholar
  • Davison, A., D. Hinkley 1997: Bootstrap Methods and their Application. - Cambridge University Press, p. 582.

    Bootstrap Methods and their Application. , () 582.

  • Efron, B. 1979: Bootstrap methods: Another look at the jackknife. - Ann. Stat., 7, pp. 1-26.

    'Bootstrap methods: Another look at the jackknife. ' () 7 Ann. Stat. : 1 -26.