caa a22 4500 469064358 CHVBK 20180323132903.0 cr unu---uuuuu 170328e19920101xx s 000 0 eng 10.1007/BF00890092 doi (NATIONALLICENCE)springer-10.1007/BF00890092 Armstrong M. Centre de Géostatistique, Ecole Nationale Superieure des Mines de Paris, 35 Rue St. Honore, 77305, Fontainebleau, France aut Positive definiteness is not enough [Elektronische Daten] [M. Armstrong] Geostatisticians know that the mathematical functions chosen to represent spatial covariances and variograms must have the appropriate type of positive definiteness, but they may not realize that there are restrictions on the types of covariances and variograms that are compatible with particular distributions. This paper gives some examples showing that (1) the spherical model is not compatible with the multivariate lognormal distribution if the coefficient of variation is 2.0 or more (even in 1-D), and (2) the Gaussian covariance and several other models are not compatible with indicator random functions. As these examples concern quite different types of random functions, it is clear that there is a general problem of compatibility between spatial covariance models (or variograms) and a specified multivariate distribution. The problem arises with all distributions except the multivariate normal, and not just the two cited here. The need for a general theorem giving the necessary and sufficient conditions for a covariance or a variogram to be compatible with a particular distribution is stressed. International Association for Mathematical Geology, 1992 positive definiteness nationallicence variogram nationallicence lognormal nationallicence indicator functions nationallicence Bochner's theorem nationallicence Mathematical Geology Kluwer Academic Publishers-Plenum Publishers 24/1(1992-01-01), 135-143 0882-8121 24:1<135 1992 24 11004 https://doi.org/10.1007/BF00890092 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00890092 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Armstrong M. Centre de Géostatistique, Ecole Nationale Superieure des Mines de Paris, 35 Rue St. Honore, 77305, Fontainebleau, France aut NATIONALLICENCE 773 0- Mathematical Geology Kluwer Academic Publishers-Plenum Publishers 24/1(1992-01-01), 135-143 0882-8121 24:1<135 1992 24 11004 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer