Abstract
Non linear problems such as change of support and estimating recoverable reserves cannot be solved without using bivariate distributions. This leads to a question concerning the consistency of these models: for a given system of bivariate distributions, does a random function which could be compatible with this system, really exist? Going further, which class of covariances is compatible with a given univariate distribution? The condition under which a covariance function is the covariance of a random set, and of a lognormal random function are considered in detail. Only partial answers and some counter-examples are presented here. The models currently available, where these consistency conditions are automatically satisfied, are réviewed.
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Matheron, G. (1989). The Internal Consistency of Models in Geostatistics. In: Armstrong, M. (eds) Geostatistics. Quantitative Geology and Geostatistics, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-6844-9_2
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DOI: https://doi.org/10.1007/978-94-015-6844-9_2
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