共查询到20条相似文献，搜索用时 15 毫秒
1.
Björn A. Malmgren 《Mathematical Geology》1979,11(3):285-297
Data of a microfossil group, the planktonic foraminifera, have been tested to determine the conformity of various real data distributions to univariate and multivariate normality and the effects that standard transformations have upon the distributions. Studies of two bivariate samples, one trivariate sample, and two quadrivariate samples of size data indicate that distributions frequently deviate greatly from multivariate normality. Univariate distributions are generally positively skewed and show a tendency for leptokurtosis. A logarithmic transformation improved both univariate and multivariate distributions but the number of distributions conformable to normality increased only slightly—from zero to one in the multivariate case and from one to four in the univariate case (totally 15 distributions). Arcsine (p/100)
1/2
transformations of percentage data in two samples including 16 and 23 species, respectively, decreased highly significant deviations from multivariate normality but distributions remained greatly non-normal. Although markedly positively skewed and leptokurtic univariate distributions were improved in most instances, the number of normal distributions (two) did not change. It follows that neither of the transformations caused significant increases in the number of normal distributions but if it is assumed that the consequences of non-normality are less severe as the deviation from normality decreases, the transformations are justified. 相似文献
2.
On unbiased backtransform of lognormal kriging estimates 总被引：4，自引：0，他引：4
Jorge Kazuo Yamamoto 《Computational Geosciences》2007,11(3):219-234
Lognormal kriging is an estimation technique that was devised for handling highly skewed data distributions. This technique
takes advantage of a logarithmic transformation that reduces the data variance. However, backtransformed lognormal kriging
estimates are biased because the nonbias term is totally dependent on a semivariogram model. This paper proposes a new approach
for backtransforming lognormal kriging estimates that not only presents none of the problems reported in the literature but
also reproduces the sample histogram and, consequently, the sample mean. 相似文献
3.
N. H. WOODCOCK 《Sedimentology》1979,26(1):83-99
The two main methods of estimating palaeoslope direction from slump structure orientation data are reviewed. The mean axis method takes the downslope direction as the perpendicular to the mean slump fold axis. The separation are method estimates the downslope direction by the bisector of a planar separation angle between groups of slump folds with opposite downplunge asymmetry. The advantages and disadvantages of each method are considered in detail, by reference first to idealized slump fold distributions and then to a compilation of sixty natural slump fold axis distributions, mostly from published data. Among the advantages of the mean axis method are the ease of deriving confidence limits for estimates and its applicability where fold asymmetry data are unavailable. The main advantage of the separation are method is its validity for strongly skewed fold axis samples. The statistical robustness of the mean axis method, however, due to its reliance on average properties of data, makes it more generally reliable than the separation arc method which depends on extreme properties of data. A procedure for determining palaeoslope directions is suggested which reflects the respective strengths of the two methods. 相似文献
4.
Environmental data seldom follow normal distributions, so how to calculate their means is a very important problem. Commonly used methods for mean calculation, such as arithmetic mean, geometric mean, and median, were evaluated. Arithmetic means should only be used when datasets follow normal distributions. Geometric means are suitable for datasets which follow log-normal distributions. Medians are a kind of robust treatment. However, their efficiency is very low. Based on the methods described, two new ideas are developed: robust and symmetric, for calculating means. As far as the symmetric feature is concerned, Box-Cox power transformation is better than logarithmic transformation. Robust statistics and Box-Cox transformation are combined to produce the robust-symmetric mean. As environmental data often follow log-normal or skewed distributions, this method is better than the previous ones and also is appropriate. 相似文献
5.
Analysis of bimodal orientation data 总被引：1，自引：0，他引：1
Statistical models underlying the analysis of orientation data commonly assume a unimodal symmetric population, such as the circular normal distribution. If the sample distribution is skewed or bimodal, standard procedures usually produce misleading results. Where such situations occur, a mixture of two or more circular normal distributions may be used as the population model. The parameters describing each mode and the mixing proportion may be estimated by the method of maximum likelihood using numerical techniques. This approach is applied to a distinctly bimodal set of cross-bedding data from the Mississippian Salem Limestone of central Indiana. 相似文献
6.
Normal and lognormal data distribution in geochemistry: death of a myth. Consequences for the statistical treatment of geochemical and environmental data 总被引：13，自引：0，他引：13
All variables of several large data sets from regional geochemical and environmental surveys were tested for a normal or
lognormal data distribution. As a general rule, almost all variables (up to more than 50 analysed chemical elements per data
set) show neither a normal or a lognormal data distribution. Even when different transformation methods are used more than
70 % of all variables in every single data set do not approach a normal distribution. Distributions are usually skewed, have
outliers and originate from more than one process. When dealing with regional geochemical or environmental data normal and/or
lognormal distributions are an exception and not the rule. This observation has serious consequences for the further statistical
treatment of geochemical and environmental data. The most widely used statistical methods are all based on the assumption
that the studied data show a normal or lognormal distribution. Neglecting that geochemcial and environmental data show neither
a normal or lognormal distribution will lead to biased or faulty results when such techniques are used.
Received: 21 June 1999 · Accepted: 14 August 1999 相似文献
7.
《Applied Geochemistry》2004,19(6):887-898
Castromil is one of the Au mining areas in Portugal that has been abandoned since 1940. Due to the lack of regulations and environmental education, Castromil is now a residential area suffering from the considerable consequences of poorly regulated mining activities; tailings, shafts and adits are present. Geochemical data related to environmental studies in old mining areas frequently show extremely high values and very skewed distributions that need to be properly addressed. Agricultural soils from this region have high concentrations of As and Pb. In this study, the Box–Cox transformation and geostatistics were applied to study heavy element (As and Pb) concentrations in soils in order to characterize the hazard posed by them in the area. This provides a decision support tool to define the areas where remedial action is needed in light of the risks to humans and ecosystems and for contaminant migration. The results discussed here take into account the hazard-based standards for soils as target and intervention values. 相似文献
8.
Cluster analysis can be used to group samples and to develop ideas about the multivariate geochemistry of the data set at hand. Due to the complex nature of regional geochemical data (neither normal nor log-normal, strongly skewed, often multi-modal data distributions, data closure), cluster analysis results often strongly depend on the preparation of the data (e.g. choice of the transformation) and on the clustering algorithm selected. Different variants of cluster analysis can lead to surprisingly different cluster centroids, cluster sizes and classifications even when using exactly the same input data. Cluster analysis should not be misused as a statistical “proof” of certain relationships in the data. The use of cluster analysis as an exploratory data analysis tool requires a powerful program system to test different data preparation, processing and clustering methods, including the ability to present the results in a number of easy to grasp graphics. Such a tool has been developed as a package for the R statistical software. Two example data sets from geochemistry are used to demonstrate how the results change with different data preparation and clustering methods. A data set from S-Norway with a known number of clusters and cluster membership is used to test the performance of different clustering and data preparation techniques. For a complex data set from the Kola Peninsula, cluster analysis is applied to explore regional data structures. 相似文献
9.
M. SANKAR DAS 《Geostandards and Geoanalytical Research》1979,3(2):199-205
Trace element data compiled on, geoshemical reference samples present invariably skewed distributions. It is proposed to treat such data as lognormally distributed and to compute geometric means (Xgm ) as probable values. As examples, the Xgm values derived for some trace elements in some rock reference samples are compared with the "recommended" values and with the "gamma" values of Christie. 相似文献
10.
Most approaches in statistical spatial prediction assume that the spatial data are realizations of a Gaussian random field.
However, this assumption is hard to justify for most applications. When the distribution of data is skewed but otherwise has
similar properties to the normal distribution, a closed skew normal distribution can be used for modeling their skewness.
Closed skew normal distribution is an extension of the multivariate skew normal distribution and has the advantage of being
closed under marginalization and conditioning. In this paper, we generalize Bayesian prediction methods using closed skew
normal distributions. A simulation study is performed to check the validity of the model and performance of the Bayesian spatial
predictor. Finally, our prediction method is applied to Bayesian spatial prediction on the strain data near Semnan, Iran.
The mean-square error of cross-validation is improved by the closed skew Gaussian model on the strain data. 相似文献
11.
A previously described method of combining measurements of numerous pebble cross-sections in three orthogonal planes into a single average ellipsoid was found to be in need of improvement. The method of reconciling redundancies and of distributing the errors can be left unchanged. The original measurements of principal half-axes, however, rather than being normalized as the ratios of larger half-axes divided by the smaller, should be normalized so that they produce ellipses of standard area. The coefficients of ellipses so normalized will produce distributions with a pronounced central tendency even in those cases that produce markedly skewed distributions of coefficients for ellipses normalized by the former method. Equations of the previous paper that must be amended are given in their new form. 相似文献
12.
Chunfa Wu Jiaping Wu Yongming Luo Haibo Zhang Ying Teng Stephen D. DeGloria 《Environmental Earth Sciences》2011,63(5):1093-1103
It was not unusual in soil and environmental studies that the distribution of data is severely skewed with several high peak
values, which causes the difficulty for Kriging with data transformation to make a satisfied prediction. This paper tested
an approach that integrates kriging and triangular irregular network interpolation to make predictions. A data set consisting
of total Copper (Cu) concentrations of 147 soil samples, with a skewness of 4.64 and several high peak values, from a copper
smelting contaminated site in Zhejiang Province, China. The original data were partitioned into two parts. One represented
the holistic spatial variability, followed by lognormal distribution, and then was interpolated by lognormal ordinary kriging.
The other assumed to show the local variability of the area that near to high peak values, and triangular irregular network
interpolation was applied. These two predictions were integrated into one map. This map was assessed by comparing with rank-order
ordinary kriging and normal score ordinary kriging using another data set consisting of 54 soil samples of Cu in the same
region. According to the mean error and root mean square error, the approach integrating lognormal ordinary kriging and triangular
irregular network interpolation could make improved predictions over rank-order ordinary kriging and normal score ordinary
kriging for the severely skewed data with several high peak values. 相似文献
13.
N. H. Trewin 《Geological Journal》1973,8(2):307-316
Size sorting of shells and valves of transported death assemblages of Mytilus edulis is shown to have taken place, and greatly affected size-frequency distributions of shell accumulations deposited in a beach environment. Selective transport and deposition of different size grades gives histograms which may be strongly skewed or multimodal, and include numerous small shells. The usually predicted bell-shaped distributions for sorted assemblages are not always produced. Little evidence of growth and mortality rates can be deduced with confidence from the transported assemblages. 相似文献
14.
R. P. Chapman 《Mathematical Geology》1978,10(2):195-224
Univariate and multivariate statistical methods were evaluated using published multi-element stream sediment data from southwestern and northern New Brunswick. The statistical distributions of elements do not obey Ahrens' law of lognormality; eleven of thirteen elements investigated for the Bathurst-Jacquet River area are not lognormally distributed at the 0.05 level of significance. The distributions are positively skewed and leptokurtic and consist of aggregate populations which represent mineral deposits, bedrock, and many other physiographic factors; some of these populations are normally distributed. The efficiency of the Pearson correlation coefficient varied and was compared to nonparametric correlation. Various methods of factor analysis were evaluated and the structure of the factors was similar to the subjective groupings derived from the correlation matrices. Comparison of correlation coefficients and factor models derived from the log-transformed and untransformed Bathurst-Jacquet River data showed that background associations were enhanced by the log transformation at the expense of associations representing mineralization. Q-mode factor matrices could not be satisfactorily interpreted without recourse to the mapping of the factor loadings. The maps produced were inferior to simple concentration maps. An iterative technique was developed for discriminant analysis to refine the sample training groups representing mineralized and background terrain; repeated discriminant analysis after misclassified samples were eliminated altered the inherent character of the training groups. Trend surface analysis was found to give goodness of fits of the trend equations comparable to the fits expected from random numbers. The method was mathematically inappropriate for the type of data used. The goal of exploration geochemical statistical analysis should be to discriminate and sort populations representing mineralized and background populations by classification or filtering techniques. 相似文献
15.
This paper presents a modified ordinary kriging technique referred to as the “Area Influence Kriging” (AIK). The method is a simple and practical tool to use for more accurate prediction of global recoverable ore resources in any type of deposit. AIK performs well even in deposits with skewed grade distributions when the ordinary kriging (OK) results are unreasonably smooth. It is robust and globally unbiased like OK. The AIK method is not intended to replace OK, which is a better estimator of the average grade of the blocks. Rather it aims to complement OK with its excellent performance in predicting recoverable resources that have been the major pitfalls of OK in many resource estimation cases. The paper details the methodology of AIK with a couple of examples. It also reports the results from its application to a gold deposit. 相似文献
16.
Gilles Bourgault 《Mathematical Geosciences》2014,46(7):841-868
A multivariate probability transformation between random variables, known as the Nataf transformation, is shown to be the appropriate transformation for multi-Gaussian kriging. It assumes a diagonal Jacobian matrix for the transformation of the random variables between the original space and the Gaussian space. This allows writing the probability transformation between the local conditional probability density function in the original space and the local conditional Gaussian probability density function in the Gaussian space as a ratio equal to the ratio of their respective marginal distributions. Under stationarity, the marginal distribution in the original space is modeled from the data histogram. The stationary marginal standard Gaussian distribution is obtained from the normal scores of the data and the local conditional Gaussian distribution is modeled from the kriging mean and kriging variance of the normal scores of the data. The equality of ratios of distributions has the same form as the Bayes’ rule and the assumption of stationarity of the data histogram can be re-interpreted as the gathering of the prior distribution. Multi-Gaussian kriging can be re-interpreted as an updating of the data histogram by a Gaussian likelihood. The Bayes’ rule allows for an even more general interpretation of spatial estimation in terms of equality for the ratio of the conditional distribution over the marginal distribution in the original data uncertainty space with the same ratio for a model of uncertainty with a distribution that can be modeled using the mean and variance from direct kriging of the original data values. It is based on the principle of conservation of probability ratio and no transformation is required. The local conditional distribution has a variance that is data dependent. When used in sequential simulation mode, it reproduces histogram and variogram of the data, thus providing a new approach for direct simulation in the original value space. 相似文献
17.
A. COLOMBO 《Geostandards and Geoanalytical Research》1980,4(2):239-242
A method which consists essentially in ranking and then plotting on rectangular coordinates the data of a skewed set of results to the purpose of identifying the modal value of the set, is described. The method is simple, fast (if a plotter is used) and requires no calculations. 相似文献
18.
The Folk&Ward (F&W) and the log-hyperbolic methods are applied to a small - and easy to overlook - number of typical sand sized grain-size distributions from the Danish Wadden Sea. The sand originates from the same source, and the pattern of change in the grain-size distributions is, therefore, exclusively linked to dynamic sorting. In general, the F&W parameters reflect the observed grain-size trends far better than the corresponding log-hyperbolic parameters. The log-hyperbolic “typical log grain size”, ν, is sensitive to changes in skewness and cannot replace mean grain size, Mz, in grain-size trend analysis. The four log-hyperbolic parameters describing dispersion δ, τ− 1, κ− 1 and ζ are not able to give an unambiguous picture of spreading trends. The F&W sorting parameter, Sd, can therefore not be replaced by any of the log-hyperbolic parameters in grain-size trend analysis. In skewed grain-size distributions, there seems to be a general defect in the log-hyperbolic approximation of the best represented tail. This makes χ less sensitive to indicate the correct sign of slightly skewed grain-size distributions than Sk. However, when examining trends, the relative change between χ and Sk by and large seems to be the same. The log-hyperbolic peakedness parameter, ξ, is preferable to the F&W peakedness (kurtosis) parameter, Kg, because the latter is hypersensitive to small, insignificant variations in a grain-size distribution. By contrast, the concept of peakedness as defined by ξ, seems to relate more directly to sedimentary environmental conditions. In conclusion, the log-hyperbolic method has both advantages and disadvantages when compared with the F&W method. It is thus suggested that a sensible combination of the two methods could be advantageous to sediment trend analysis. 相似文献
19.
The formal stereological transformation equation for particle sieve size distribution from measurements in lower dimensional spaces is applied to laser diffractometer measurements. The transformation function for iron ore particles is measured experimentally, and modeled. The solution is tested against the measured transformation function data as well as synthetic composite distributions of the original sample. The natural size distribution of a sample taken from a grinding circuit stream was measured by a combination of standard sieving and cyclosizer, and the result is compared to the transformed size distribution calculated from laser diffractometer measurements. The stereological transformation technique performed well in all cases. 相似文献
20.
Ajay Jasra David A. Stephens Kerry Gallagher Christopher C. Holmes 《Mathematical Geology》2006,38(3):269-300
In this paper we develop a generalized statistical methodology for characterizing geochronological data, represented by a distribution of single mineral ages. The main characteristics of such data are the heterogeneity and error associated with its collection. The former property means that mixture models are often appropriate for their analysis, in order to identify discrete age components in the overall distribution. We demonstrate that current methods (e.g., Sambridge and Compston, 1994) for analyzing such problems are not always suitable due to the restriction of the class of component densities that may be fitted to the data. This is of importance, when modelling geochronological data, as it is often the case that skewed and heavy tailed distributions will fit the data well. We concentrate on developing (Bayesian) mixture models with flexibility in the class of component densities, using Markov chain Monte Carlo (MCMC) methods to fit the models. Our method allows us to use any component density to fit the data, as well as returning a probability distribution for the number of components. Furthermore, rather than dealing with the observed ages, as in previous approaches, we make the inferences of components from the “true” ages, i.e., the ages had we been able to observe them without measurement error. We demonstrate our approach on two data sets: uranium-lead (U-Pb) zircon ages from the Khorat basin of northern Thailand and the Carrickalinga Head formation of southern Australia. 相似文献