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Bivariate Distribution
Conditional Expectation
Continuous Variable
Correlation Coefficient
cumulant
Gaussian Distribution
Multivariate Statistics
Outlier Detection
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Plotting and checking the bivariate distributions of multiple Gaussian data
Plotting and checking the bivariate distributions of multiple Gaussian data,10.1016/j.cageo.2011.01.014,Computers & Geosciences,Jared L. Deutsch,Clayt
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Plotting and checking the bivariate distributions of multiple Gaussian data
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Jared L. Deutsch
,
Clayton V. Deutsch
The geostatistical modeling of continuous variables relies heavily on the multivariate Gaussian distribution. It is remarkably tractable. The multivariate
Gaussian distribution
is adopted for K multiple variables (often K is between 2 and 10) and for N multiple locations (often N is in the tens of millions). Our focus is on the relationship between the K variables. Each variable is transformed to be univariate Gaussian, but the multivariate nature of the data is not necessarily Gaussian after univariate transformation. If multiple data variables are deemed nonGaussian, then additional steps need to be taken such as linearization by alternating
conditional expectation
(ACE) or multivariate transformation by the stepwise conditional transformation (SCT). Although all Lvariate distributions (1<L≤K) should be checked, the bivariate distributions are practically important; there are relatively few data in practice to investigate
higher order
distributions. A quantitative measure of departure from the bivariate
Gaussian distribution
is established based on quadrants and the distribution of differences from the theoretically expected distribution. Although approximate, the measure of departure is useful for comparing different distributions and guiding the geostatistician to look closer at some data variables. A scatnscores program is shown that will plot all K(K–1)/2 bivariate cross plots associated with K variables. The correlation coefficients, number of data, degree of departure from the bivariate Gaussian distribution, and bivariate Gaussian probability contours associated with specified cumulative probabilities are shown. The data ID numbers can also be shown to help identify outlier or problematic data.
Journal:
Computers & Geosciences  COMPUT GEOSCI
, vol. 37, no. 10, pp. 16771684, 2011
DOI:
10.1016/j.cageo.2011.01.014
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