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Previous research has shown that people err when making decisions aided by probability information. Surprisingly, there has been little exploration into the accuracy of decisions made based on many commonly used probabilistic display methods. Two experiments examined the ability of a comprehensive set of such methods to effectively communicate critical information to a decision maker and influence confidence in decision making. The second experiment investigated the performance of these methods under time pressure, a situational factor known to exacerbate judgmental errors. Ten commonly used graphical display methods were randomly assigned to participants. Across eight scenarios in which a probabilistic outcome was described, participants were asked questions regarding graph interpretation (e.g., mean) and made behavioral choices (i.e., act; do not act) based on the provided information indicated that decision-maker accuracy differed by graphical method; error bars and boxplots led to greatest mean estimation and behavioral choice accuracy whereas complementary cumulative probability distribution functions were associated with the highest probability estimation accuracy. Under time pressure, participant performance decreased when making behavioral choices. [ABSTRACT FROM AUTHOR]

This article presents a Python‐based package, ipyChord, to compute the 2D chord distribution function (CDF) from the small‐angle X‐ray scattering (SAXS) pattern from polymer materials with fiber‐symmetrical nanostructure. The program allows construction of a harmonized SAXS pattern from a raw SAXS pattern, by normalization of the incident‐beam intensity, absorption correction for sample thickness, masking blind areas on the detector, and filling in the shadow of the beamstop and its holder using symmetry operations. Patterns from modular detectors with inter‐module gaps can still be fully constructed satisfactorily after determining the optimized beam position and a radial basis function. A CDF pattern computed from the full SAXS pattern can be used to determine the domain size and its variability using a graphical method. An interface distribution function computed from Bonart's longitudinal projection or sliced from a CDF meridian can quantify differently stacked hard and soft domains. Two cases of the application of ipyChord are presented. The software is open source and available at https://github.com/isaxs/ipyChord. [ABSTRACT FROM AUTHOR]

A random effects model using two levels of hierarchical nesting has been applied to the calculation of a likelihood ratio as a solution to the problem of comparison between two sets of replicated multivariate continuous observations where it is unknown whether the sets of measurements shared a common origin. Replicate measurements from a population of such measurements allow the calculation of both within-group and between-group variances/covariances. The within-group distribution has been modelled assuming a Normal distribution, and the between-group distribution has been modelled using a kernel density estimation procedure. A graphical method of estimating the dependency structure among the variables has been used to reduce this highly multivariate problem to several problems of lower dimension. The approach was tested using a database comprising measurements of eight major elements from each of four fragments from each of 200 glass objects and found to perform well compared with previous approaches, achieving a 15.2% false-positive rate, and a 5.5% false-negative rate. The modelling was then applied to two examples of casework in which glass found at the scene of the criminal activity has been compared with that found in association with a suspect. [ABSTRACT FROM AUTHOR]

This note provides a statistical-graphical method for the evaluation of the statistical significance of difference potentials from a group of subjects, and for the comparison of difference potentials between two groups. A table of the lengths of statistically significant intervals for various sampling interval lengths, numbers of subjects, and autocorrelation parameters is presented. [ABSTRACT FROM AUTHOR]

Duplicate analysis is a strategy commonly used to assess precision of bioanalytical methods. In some cases, duplicate analysis may rely on pooling data generated across organizations. Despite being generated under comparable conditions, organizations may produce duplicate measurements with different precision. Thus, these pooled data consist of a heterogeneous collection of duplicate measurements. Precision estimates are often expressed as relative difference indexes (RDI), such as relative percentage difference (RPD). Empirical evidence indicates that the frequency distribution of RDI values from heterogeneous data exhibits sharper peaks and heavier tails than normal distributions. Therefore, traditional normal‐based models may yield faulty or unreliable estimates of precision from heterogeneous duplicate data. In this paper, we survey application of the mixture models that satisfactorily represent the distribution of RDI values from heterogeneous duplicate data. A simulation study was conducted to compare the performance of the different models in providing reliable estimates and inferences of percentile calculated from RDI values. These models are readily accessible to practitioners for study implementation through the use of modern statistical software. The utility of mixture models are explained in detail using a numerical example. [ABSTRACT FROM AUTHOR]

Bias correction methods are used to adjust simulations from global and regional climate models to use them in informed decision‐making. Here we introduce a semi‐parametric quantile mapping (SPQM) method to bias‐correct daily precipitation. This method uses a parametric probability distribution to describe observations and an empirical distribution for simulations. Bias‐correction techniques typically adjust the bias between observation and historical simulations to correct projections. The SPQM however corrects simulations based only on observations assuming the detrended simulations have the same distribution as the observations. Thus, the bias‐corrected simulations preserve the climate change signal, including changes in the magnitude and probability dry, and guarantee a smooth transition from observations to future simulations. The results are compared with popular quantile mapping techniques, that is, the quantile delta mapping (QDM) and the statistical transformation of the CDF using splines (SSPLINE). The SPQM performed well in reproducing the observed statistics, marginal distribution, and wet and dry spells. Comparatively, it performed at least equally well as the QDM and SSPLINE, specifically in reproducing observed wet spells and extreme quantiles. The method is further tested in a basin‐scale region. The spatial variability and statistics of the observed precipitation are reproduced well in the bias‐corrected simulations. Overall, the SPQM is easy to apply, yet robust in bias‐correcting daily precipitation simulations. Plain Language Summary: Climate models help project changes in precipitation. Yet their simulations show bias from observed data. In this study, we proposed a robust bias‐correction method, semi‐parametric quantile mapping (SPQM), to adjust the simulations, such that they statistically match observed data. The method also adjusts the probability of dry days in bias‐corrected simulations. For the future, the trend line of the observed wet/dry time series is maintained. We compared our method with the two most popularly used quantile mapping methods. Comparatively, the SPQM performed well in matching the observed distribution, wet/dry spells, and statistics in bias‐corrected simulations. We further used this method in a basin‐scale application and found that the observed spatial variability in precipitation is reproduced well. Key Points: A novel bias‐correction method, semi‐parametric quantile mapping (SPQM), is introducedBias‐corrected simulations using SPQM preserved observed marginal distribution, wet and dry spells, and reproduced observed statisticsSPQM performed equally well or better than widely used quantile mapping methods, in reproducing observed wet spells and extreme quantiles [ABSTRACT FROM AUTHOR]

The degree of inter‐rater agreement is usually assessed through κ‐type coefficients and the extent of agreement is then characterized by comparing the value of the adopted coefficient against a benchmark scale. Through two motivating examples, it is displayed the different behavior of some κ‐type coefficients due to asymmetric distribution of marginal frequencies over categories. In order to investigate the robustness of four κ‐type coefficients for nominal and ordinal classifications and of an inferential benchmarking procedure that, differently from straightforward benchmarking, does not neglect the influence of the experimental conditions, an extensive Monte Carlo simulation study has been conducted. The robustness has been investigated for several scenarios, differing for sample size, rating scale dimension, number of raters, frequency distribution of rater classifications, pattern of agreement across raters. Simulation results reveal an higher paradoxical behavior of Fleiss kappa and Conger kappa with ordinal rather than nominal classifications; the coefficients robustness improves with increasing sample size and number of raters for both nominal and ordinal classifications whereas robustness improves with rating scale dimension only for nominal classifications. By identifying the scenarios (ie, minimum sample size, number of raters, rating scale dimension) with acceptable robustness, this study provides guidelines about the design of robust agreement studies. [ABSTRACT FROM AUTHOR]

The increasing sophistication of wind turbine design and control generates a need for high‐quality wind data. The relatively limited set of available measured wind data may be extended with computer generated data, for example, to make reliable statistical studies of energy production and mechanical loads. Here, a data‐driven model for the generation of surrogate wind speeds is compared with two state‐of‐the‐art time series models that can capture the probability distribution and the autocorrelation of the target wind data. The proposed model, based on the phase‐randomised Fourier transform, can generate wind speed time series that possess the power spectral density of the target data and converge to their generally non‐Gaussian probability distribution with an arbitrary, user‐defined precision. The model performance is benchmarked in terms of probability distribution, power spectral density, autocorrelation, and nonstationarities such as the diurnal and seasonal variations of the target data. Comparisons show that the proposed model can outperform the selected models in reproducing the statistical descriptors of the input datasets and is able to capture the nonstationary diurnal and seasonal variations of the wind speed. [ABSTRACT FROM AUTHOR]

Extreme precipitation events lie in the upper part of the probability distribution of daily precipitation data, that is, the tail. Depending upon the tail behaviour, various probability distributions are partitioned into heavy‐tailed and light‐tailed distributions. Heavy‐tails tend to approach zero less rapidly than light‐tails, signifying a higher frequency of occurrences for extreme precipitation events. Prediction of extreme precipitation depends on how reliably the distribution tail is modelled. Tail behaviour can be studied by graphical as well as threshold‐based fitting approaches. However, the graphical methods are time‐consuming and do not provide quantitative comparisons between two distributions, whereas the threshold‐based approaches possess limitations such as ambiguity in selecting an optimum threshold for demarcation of the tail. This article assesses the utility of a simple empirical index, that is, the "Obesity Index" (OB) to discern the probability distributions of daily gridded precipitation data with a resolution of 0.25° for historical (1951–2004) and future (2006–2099) periods over India into light‐ and heavy‐tailed. The OB‐based approach is an easy‐to‐use empirical approach that can quantitatively diagnose the heaviness of distribution tails without assuming any threshold for segregating the tails. Future projections of daily precipitation were obtained by downscaling simulations of the Coordinated Regional Climate Downscaling Experiment. Subsequently, a comparative analysis between the OB‐based approach and threshold‐based approaches by Nerantzaki and Papalexiou and Papalexiou et al. was conducted. Finally, the application of the OB‐based approach is extended to characterize daily precipitation in Indian Meteorological Subdivisions. Furthermore, we explored the dependence of the OB on the elevation of grids. Results indicated the applicability of heavy‐tailed distributions in the representation of daily precipitation over India and suggest an OB‐based approach as a good alternative diagnostic tool for assessing tail behaviour. [ABSTRACT FROM AUTHOR]

A warming climate is associated with increasing hydroclimatic extremes, which are often interconnected through complex processes, prompting their concurrence and/or succession, and causing compound extreme events. It is critical to analyze the risks of compound events, given their disproportionately high adverse impacts. To account for the variability in two or more hydroclimatic variables (e.g., temperature and precipitation) and their dependence, a rising number of publications focuses on multivariate analysis, among which the notion of copula‐based probability distribution has attracted tremendous interest. Copula is a mathematical function that expresses the joint cumulative probability distribution of multiple variables. Our focus is to re‐emphasize the fundamental requirements and limitations of applying copulas. Confusion about these requirements may lead to misconceptions and pitfalls, which can potentially compromise the robustness of risk analyses for environmental processes and natural hazards. We conducted a systematic literature review of copulas, as a prominent tool in the arsenal of multivariate methods used for compound event analysis, and underpinned them with a hydroclimatic case study in Sweden to illustrate a practical approach to copula‐based modeling. Here, we (1) provide end‐users with a didactic overview of necessary requirements, statistical assumptions and consequential limitations of copulas, (2) synthesize common perceptions and practices, and (3) offer a user‐friendly decision support framework to employ copulas, thereby support researchers and practitioners in addressing hydroclimatic hazards, hence demystify what can be an area of confusion. This article is categorized under:Science of Water > Hydrological ProcessesScience of Water > Methods [ABSTRACT FROM AUTHOR]

For any given multivariate distribution, explicit formulae for the asymptotic covariances of cumulant vectors of the third and the fourth order are provided here. General expressions for cumulants of elliptically symmetric multivariate distributions are also provided. Utilizing these formulae one can extend several results currently available in the literature, as well as obtain practically useful expressions in terms of population cumulants, and computational formulae in terms of commutator matrices. Results are provided for both symmetric and asymmetric distributions, when the required moments exist. New measures of skewness and kurtosis based on distinct elements are discussed, and other applications to independent component analysis and testing are considered. [ABSTRACT FROM AUTHOR]

Glass plies can be bonded together by polymeric interlayers to form laminated glass. Thanks to the capacity in finding alternative stress paths after partial breakage, it is commonly accepted that the more the layers are, the higher the safety level is. However, a negative aspect is that the tensile strength of glass carries a size effect in terms of surface area, which increases with lamination. Here we evaluate these competing factors by calibrating the partial safety factors to be used in semi‐probabilistic (level‐I) design, through comparison with probabilistic (level‐III) methods in paradigmatic case‐studies under wind, snow, and dead weight. Starting from a two‐parameter Weibull distribution for glass strength, the "failure modes" approach determines the statistical distribution of strength for a multi‐laminate as a function of the number of plies, which interferes with the statistics for actions. As a function of the target probability of failure for the assigned class of consequence, we introduce a new coefficient in the verification formula of level‐I, to account for the effects of lamination with dependence upon the number of plies. We find that there is strong gain when passing from a monolith to a two‐ply laminate, but the advantage fades by increasing the number of layers. Verification formulas of this type could avoid overconservative design. [ABSTRACT FROM AUTHOR]

Good practice in smart grids is networked sensors topologies which give the ability to fuse sensors to obtain a new feature based on sensors' complementarity. Moreover, to get a prediction based on other sensors, possibly in other areas, in case of sensor failure. This ability may be achieved by correlating sensor data based on their historical observations. This study addresses the problem of stochastic multivariate modelling within the framework of cyber-physical systems. Weibull distribution function (WDF) was found to be the best probability distribution function to fit wind variations. The main idea of this study is to propose a generalised multivariate stochastic model to describe the joint probability between multi-stochastic variables. A novel multivariate WDF for wind modelling is proposed to estimate wind speed in one location based on wind speed data on other location(s). The suggested approach is applied to three cases to demonstrate the efficacy of the developed technique. It is pointed out that this approach could be generalised for the multivariate WDF of wind modelling situations. Finally, it is shown that there are existing structures resemblances between the wind Weibull versus normal distribution models arising from the fact WDF reflects a natural phenomenon with some restrictions. [ABSTRACT FROM AUTHOR]

For smart electricity meter with multiple performance characteristics (PCs) with coupling relationships because of amounts of components experiencing multiple deteriorating processes, we develop a multivariate degradation modeling method via vine copulas to estimate the reliability of products with multiple PCs reflecting degradation states. In the multivariate model, pair-copula construction and vine graphical representation are used to describe the mutual relationship among PCs to overcome the lack of multivariate copula in high-dimensional cases. Each PC model of smart electricity meter is built by using drift Brownian motion to describe degradation processes of each PC on the basis of degradation mechanism analysis, and parameters are estimated by using likelihood estimation method. The Pearson correlation coefficient, Kendall's τ and product information are used to analyze correlation among those PCs. Furthermore, on the basis of conditional probability theory, the vine graph is used to construct a multivariate copula which can be decomposed into pair copulas. Akaike information criterion principle is utilized to choose the forms of pair-copula functions in the correlation model. Finally, the reliability joint distribution of all PCs of smart electricity meter is obtained with combining all PCs' marginal distributions and copula functions. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Forecast verification is important across scientific disciplines, as it provides a framework for evaluating the performance of a forecasting system. In the atmospheric sciences, probabilistic skill scores are often used for verification, as they provide a way of ranking the performance of different probabilistic forecasts unambiguously. In order to be useful, a skill score must be proper: it must encourage honesty in the forecaster and reward forecasts that are reliable and have good resolution. A new score, the error-spread score (ES), is proposed, which is particularly suitable for evaluation of ensemble forecasts. It is formulated with respect to the moments of the forecast. The ES is confirmed to be a proper score and is therefore sensitive to both resolution and reliability. The ES is tested on forecasts made using the Lorenz ′96 system and found to be useful for summarizing the skill of the forecasts. The European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble prediction system (EPS) is evaluated using the ES. Its performance is compared with a perfect statistical probabilistic forecast: the ECMWF high-resolution deterministic forecast dressed with the observed error distribution. This generates a forecast that is perfectly reliable if considered over all time, but does not vary from day to day with the predictability of the atmospheric flow. The ES distinguishes between the dynamically reliable EPS forecasts and the statically reliable dressed deterministic forecasts. Other skill scores are tested and found to be comparatively insensitive to this desirable forecast quality. The ES is used to evaluate seasonal range ensemble forecasts made with the ECMWF System 4. The ensemble forecasts are found to be skilful when compared with climatological or persistence forecasts, though this skill is dependent on the region and time of year. [ABSTRACT FROM AUTHOR]

The mixed inverse Gaussian given by Whitmore (biScand. J. Statist., 13, 1986, 211-220) provides a convenient way for testing the goodness-of-fit of a pure inverse Gaussian distribution. The test is a one-sided score test with the null hypothesis being the pure inverse Gaussian (i.e. the mixing parameter is zero) and the alternative a mixture. We devise a simple score test and study its finite sample properties. Monte Carlo results show that it compares favourably with the smooth test of Ducharme ( Test, 10, 2001, 271-290). In practical applications, when the pure inverse Gaussian distribution is rejected, one is interested in making inference about the general values of the mixing parameter. However, as it is well known that the inverse Gaussian mixture is a defective distribution; hence, the standard likelihood inference cannot be applied. We propose several alternatives and provide score tests for the mixing parameter. Finite sample properties of these tests are examined by Monte Carlo simulation. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Conventional multivariate hydrological frequency analysis utilizes only the concurrent parts of data sets, leaving a lot of nonconcurrent data unutilized. Simultaneous inclusion of such nonconcurrent data can significantly reduce uncertainty in hydrologic design estimates. The methodology proposed in this paper allows varied length multivariate data to be combined and analyzed in an integrated framework through a 'Composite Likelihood Approach.' The method employs copula-based multivariate distributions in order to provide necessary flexibility of admitting arbitrary marginals. The paper presents the theoretical basis of the approach and highlights its advantages through two applications. A significant reduction in uncertainty in design flood quantiles of a relatively shorter flood series is achieved by utilizing an associated downstream flood data. The advantage of the methodology is further demonstrated by establishing significant information gain for six different combinations of Gaussian and non-Gaussian marginals. The proposed approach marks a paradigm shift in hydrologic design procedures, particularly for partially gauged basins, wherein a higher precision in hydrologic designs is achieved by leveraging associated information that has hitherto remained unutilized. It is opined that the approach will enable offsetting the impact of dwindling hydrological observation networks around the world by enhancing information that is derivable from existing networks. [ABSTRACT FROM AUTHOR]

Procedures are reviewed and recommendations made for the choice of the size of a sample to estimate the characteristics (sometimes known as parameters) of a population consisting of discrete items which may belong to one and only one of a number of categories with examples drawn from forensic science. Four sampling procedures are described for binary responses, where the number of possible categories is only two, e.g., licit or illicit pills. One is based on priors informed from historical data. The other three are sequential. The first of these is a sequential probability ratio test with a stopping rule derived by controlling the probabilities of type 1 and type 2 errors. The second is a sequential variation of a procedure based on the predictive distribution of the data yet to be inspected and the distribution of the data that have been inspected, with a stopping rule determined by a prespecified threshold on the probability of a wrong decision. The third is a two-sided sequential criterion which stops sampling when one of two competitive hypotheses has a probability of being accepted which is larger than another prespecified threshold. The fifth procedure extends the ideas developed for binary responses to multinomial responses where the number of possible categories (e.g., types of drug or types of glass) may be more than two. The procedure is sequential and recommends stopping when the joint probability interval or ellipsoid for the estimates of the proportions is less than a given threshold in size. For trinomial data this last procedure is illustrated with a ternary diagram with an ellipse formed around the sample proportions. There is a straightforward generalization of this approach to multinomial populations with more than three categories. A conclusion provides recommendations for sampling procedures in various contexts. [ABSTRACT FROM AUTHOR]

We suggest a convenient version of the omnibus test for normality, using skewness and kurtosis based on Shenton and Bowman [ Journal of the American Statistical Association (1977) Vol. 72, pp. 206–211], which controls well for size, for samples as low as 10 observations. A multivariate version is introduced. Size and power are investigated in comparison with four other tests for multivariate normality. The first power experiments consider the whole skewness–kurtosis plane; the second use a bivariate distribution which has normal marginals. It is concluded that the proposed test has the best size and power properties of the tests considered. [ABSTRACT FROM AUTHOR]

This paper develops an unconditional and conditional extreme value approach to calculating value at risk (VaR), and shows that the maximum likely loss of financial institutions can be more accurately estimated using the statistical theory of extremes. The new approach is based on the distribution of extreme returns instead of the distribution of all returns and provides good predictions of catastrophic market risks. Both the in-sample and out-of-sample performance results indicate that the Box–Cox generalized extreme value distribution introduced in the paper performs surprisingly well in capturing both the rate of occurrence and the extent of extreme events in financial markets. The new approach yields more precise VaR estimates than the normal and skewed t distributions. [ABSTRACT FROM AUTHOR]

In this article, we discuss the optimal allocation problem in a multiple stress levels life‐testing experiment when an extreme value regression model is used for statistical analysis. We derive the maximum likelihood estimators, the Fisher information, and the asymptotic variance–covariance matrix of the maximum likelihood estimators. Three optimality criteria are defined and the optimal allocation of units for two‐ and k‐stress level situations are determined. We demonstrate the efficiency of the optimal allocation of units in a multiple stress levels life‐testing experiment by using real experimental situations discussed earlier by McCool and Nelson and Meeker. Monte Carlo simulations are used to show that the optimality results hold for small sample sizes as well. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007 [ABSTRACT FROM AUTHOR]

In this paper we propose goodness-of-fit tests for Aalen's additive risk model. They are based on test statistics the asymptotic distributions of which are determined under both the null and alternative hypotheses. The results are derived using martingale techniques for counting processes. An important feature of these tests is that they can be adjusted to particular alternatives. One of the alternatives we consider is Cox's multiplicative risk model. It is perhaps remarkable that such a test needs no estimate of the baseline hazard in the Cox model. We present simulation studies which give an impression of the performance of the proposed tests. In addition, the tests are applied to real data sets. [ABSTRACT FROM AUTHOR]

Copyright of Canadian Journal of Statistics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Demonstrated equivalence between a categorical regression model based on case-control data and anI-sample semiparametric selection bias model leads to a new goodness-of-fit test. The proposed test statistic is an extension of an existing Kolmogorov–Smirnov-type statistic and is the weighted average of the absolute differences between two estimated distribution functions in each response category. The paper establishes an optimal property for the maximum semiparametric likelihood estimator of the parameters in theI-sample semiparametric selection bias model. It also presents a bootstrap procedure, some simulation results and an analysis of two real datasets. [ABSTRACT FROM AUTHOR]

Industrial and business data often contain outliers. The reasons why outliers occur can be unclear procedures for production tasks or measurement, operators who do not follow procedures, failures in production equipment or measurement equipment, the wrong type of raw material, failure in raw material, registration errors or the fact that the response is influenced by many other factors as well as the available explanatory variables. Often there is no identifiable cause for the outliers and they are considered to be an intrinsic part of the dataset. Since data are often considered pairwise, and more methods for analysing pairwise data are available if the data-generating process can be modelled by a bivariate normal distribution, there is a need for a straightforward test of bivariate normality that is robust against outliers. This paper looks at a graphical test, based on probability plotting, for assessing whether it is reasonable to assume that a bivariate dataset stems from an approximately bivariate normal distribution, where the possibility for outliers is taken into account. The robust graphical (Robug) test uses a little-known estimator of the correlation coefficient, which is demonstrated to be robust against outliers. The graphical test is illustrated using data from our practical work. First the little-known robust estimator of the correlation parameter in the bivariate normal distribution is compared with the traditional estimator, the product moment correlation coefficient, often called Pearson's r, and Spearman's rank correlation coefficient and Kendall's tau. The little-known estimator is a transformation of Kendall's tau. The comparison is partly based on theory, and partly on the simulation of observations from the bivariate normal distribution. Our conclusions are that when outliers are not an issue, Pearson's r, Spearman's coefficient and the transformation of Kendall's tau do not perform very differently in terms of bias, standard deviation and root mean square error, while Kendall's tau is too biased to be used for the purpose in question. Concerning robustness to outliers, Pearson's r is inferior to the other estimators. It seems likely that the transformation of Kendall's tau, which is far less well-known than Pearson's r and Spearman's rank correlation coefficient, is at least as good as Spearman's coefficient when the possibility of outliers must be taken into consideration. Business and industrial improvement often requires the use of information that can be extracted from multivariate data. When the multivariate normal (MVN) distribution can be used to model the data-generating process, more methods are generally available for analysing the data and providing predictions. Many datasets are naturally approximately MVN so that deviations from normality imply special causes. Thus, tests for MVN facilitate the detection of outliers. Considerable insight is gained by looking at the data singly or pairwise. Pairwise datasets that come from a process that can be modelled as MVN, can be modelled by a bivariate normal distribution. The robust graphical test in this paper is therefore also useful for assessing whether a multivariate dataset comes from an approximate MVN distribution. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Copyright of Canadian Journal of Statistics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Canadian Journal of Statistics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Canadian Journal of Statistics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Parametric approaches to the problem of the distribution of alcohol consumption have not been very successful. In this article, it is shown that regularity in distribution can be studied without making assumptions about a distribution model underlying the data. For this purpose, a method is used with which distributions are compared graphically in so-called probability plots. It appears that, up to a proper linear transformation on a logarithmic scale, a surprisingly large regularity over time can be observed between distributions taken from Dutch samples in 1970, 1981 and 1985. Equally, distributions from male and female sub-samples do not appear to differ up to a linear shift. The finding of a relative equality in distributional form is in accordance with the Ledermann model. However, the difference with the Ledermann's model is that no assumptions about the exact shape of the distributions are being made. [ABSTRACT FROM AUTHOR]

A simple method for the determination of the lengths and distribution of conduits in plant stems and petioles is described using graphical and algebraic methods. The method proposed by Skene and Balodis (1968) is shown to give improper probability distributions. The data presented by these workers for Eucalyptus 'vessels' is reinterpreted, giving different results, so far as the accuracy of the data will show. The need for great accuracy in determination of conduit lengths from injection profiles is emphasized. [ABSTRACT FROM AUTHOR]