Multivariate statistical analysis procedures often require data to be multivariate normally distributed. Many tests have been developed to verify if a sample could indeed have come from a normally distributed population. These tests do not all share the same sensitivity for detecting departures from normality, and thus a choice of test is of central importance. This study investigates through simulated data the power of those tests for multivariate normality implemented in the statistic software R and pits them against the variant of testing each marginal distribution for normality. The results of testing two-dimensional data at a level of significance α=5% showed that almost one-third of those tests implemented in R do not have a type I error below this. Other tests outperformed the naive variant in terms of power even when the marginals were not normally distributed. Even though no test was consistently better than all alternatives with every alternative distribution, the energy-statistic test always sh...

A power study of goodness-of-fit tests for multivariate normality implemented in R

Inhibitors are widely considered an efficient tool for reducing nitrogen (N) loss and improving N use efficiency, but their effectiveness is highly variable across agroecosystems. In this study, we synthesized 182 studies (222 sites) worldwide to evaluate the impacts of inhibitors (urease inhibitors [UI], nitrification inhibitors [NI] and combined inhibitors) on crop yields and gaseous N loss (ammonia [NH3] and nitrous oxide [N2O] emissions) and explored their responses to different management and environmental factors including inhibitor application timing, fertilization regime, cropping system, water management, soil properties and climatic conditions using subgroup meta‐analysis, meta‐regression and multivariate analyses. The UI were most effective in enhancing crop yields (by 5%) and reducing NH3 volatilization (by 51%), whereas NI were most effective at reducing N2O emissions (by 49%). The application of UI mitigates NH3 loss and increases crop yields especially in high NH3‐N loss scenarios, whereas NI application would minimize the net N2O emissions and the resultant environmental impacts especially in low NH3‐N loss scenarios. Alternatively, the combined application of UI and NI enables producers to balance crop production and environmental conservation goals without pollution tradeoffs. The inhibitor efficacy for decreasing gaseous N loss was dependent upon soil and climatic conditions and management practices. Notably, both meta‐regression and multivariate analyses suggest that inhibitors provide a greater opportunity for reducing fertilizer N inputs in high‐N‐surplus systems and presumably favor crop yield enhancement under soil N deficiency situations. The pursuit of an improved understanding of the interactions between plant‐soil‐climate‐management systems and different types of inhibitors should continue to optimize the effectiveness of inhibitors for reducing environmental losses while increasing productivity.

https://onlinelibrary.wiley.com/doi/pdfdirect/10.1111/gcb.16294

Global evaluation of inhibitor impacts on ammonia and nitrous oxide emissions from agricultural soils: A meta‐analysis

The power-generalized Weibull probability distribution is very often used in survival analysis mainly because different values of its parameters allow for various shapes of hazard rate such as monotone increasing/decreasing, ∩-shaped, ∪-shaped, or constant. Modified chi-squared tests based on maximum likelihood estimators of parameters that are shown to be -consistent are proposed. Power of these tests against exponentiated Weibull, three-parameter Weibull, and generalized Weibull distributions is studied using Monte Carlo simulations. It is proposed to use the left-tailed rejection region because these tests are biased with respect to the above alternatives if one will use the right-tailed rejection region. It is also shown that power of the McCulloch test investigated can be two or three times higher than that of Nikulin–Rao–Robson test with respect to the alternatives considered if expected cell frequencies are about 5.

Goodness-of-fit tests for the power-generalized weibull probability distribution

In this article, we establish recurrence relations for the single and product moments of order statistics from the power generalized Weibull (PGW) distribution due to Bagdonovac̃ius and Nikulin (2002). These recurrence relations enable computation of the means, variances and covariances of all order statistics for all sample sizes in a simple and efficient manner. By using these relations, we have obtained the means, variances and covariances of order statistics from samples of sizes up to 5 for various values of the shape and scale parameters and present them in figures.

/pdf/power-generalized-weibull-distribution-based-on-order-404w6vpyig.pdf

Power generalized Weibull distribution based on order statistics

We compared two methods for detailed individual tree measurements: single image photogrammetry (SIP), a simplified, low-cost method, and the state-of-the-art terrestrial laser scanning (TLS). Our results provide evidence that SIP can be successfully applied to obtain accurate tree architectural traits in mature forests.
 Tree crown variables are necessary in forest modelling; however, they are time consuming to measure directly, and they are measured in many different ways. We compare two methods to obtain crown variables: laser-based and image-based. TLS is an advanced technology for three-dimensional data acquisition; SIP is a simplified, low-cost method. To elucidate differences between the methods, and validate SIP accuracy and usefulness for forest research, we investigated if (1) SIP and TLS measurements are in agreement in terms of the most widely used tree characteristics; (2) differences between the SIP traits and their TLS counterparts are constant throughout tree density and species composition; (3) tree architectural traits obtained with SIP explain differences in laser-based crown projection area (CPA), under different forest densities and stand compositions; and (4) CPA modelled with SIP variables is more accurate than CPA obtained with stem diameter-based allometric models. We also examined the correspondence between local tree densities extracted from images and from field measurements. We compared TLS and SIP in a temperate pure sessile oak and mixed with Scots pine stands, in the Orleans Forest, France. Standard major axis regression was used to establish relations between laser-based and image-based tree height and diameter at breast height. Four SIP-derived traits were compared between the levels of stand density and species composition with a t test, in terms of deviations and biases to their TLS counterparts. We created a set of linear and linear mixed models (LMMs) of CPATLS, with SIP variables. Both laser-based and image-based stem diameters were used to estimate CPA with the published allometric equations; the results were then compared with the best predictive LMM, in terms of similarity with CPATLS measurement. Local tree density extracted from images was compared with field measurements in terms of basic statistics and correlation. Tree height and diameter at breast height were reliably represented by SIP (Pearson correlation coefficients r = 0.92 and 0.97, respectively). SIP measurements were affected by the stand composition factor; tree height attained higher mean absolute deviation (1.09 m) in mixed stands, compared to TLS, than in pure stands (0.66 m); crown width was more negatively biased in mixed stands (− 0.79 m), than in pure stands (− 0.05 m); and diameter at breast height and crown asymmetry were found unaffected. Crown width and mean branch angle were key SIP explanatory variables to predict CPATLS. The model was approximately 2-fold more accurate than the CPA allometric estimations with both laser-based and image-based stem diameters. SIP-derived local tree density was similar to the field-measured density in terms of mean and standard deviation (9.6 (3.5) and 9.4 (3.6) trees per plot, respectively); the correlation between both density measures was significantly positive (r = 0.76). SIP-derived variables, such as crown width, mean branch angle, branch thickness, and crown asymmetry, were useful to explain tree architectural differences under different densities and stand compositions and may be implemented in many forest research applications. SIP may also provide a coarse measure of local competition, in terms of number of neighbouring trees. Our study provides the first test in mature forest stands, for SIP compared with TLS.

/pdf/single-image-photogrammetry-for-deriving-tree-architectural-2hv5vv6z6v.pdf

Single-image photogrammetry for deriving tree architectural traits in mature forest stands: a comparison with terrestrial laser scanning

Some recent results in the theory and applications of modified chi-squared goodness-of-fit tests are briefly discussed. It seems that for the first time power of modified chi-squared type tests for the logistic and three-parameter Weibull distributions based on moment type estimators is studied. Power of different modified tests against some alternatives for equiprobable fixed or random grouping intervals, and for Neyman–Pearson classes is investigated. It is shown that power of test statistic essentially depends on the quantity of Fisher's sample information this statistic uses. Some recommendations on implementing modified chi-squared type tests are given.

Natalya Pya

Papers

A Comparative Study of Some Modified Chi-Squared Tests

Goodness-of-fit tests for the power-generalized weibull probability distribution

The Power-Generalized Weibull probability distribution and its use in survival analysis

Goodness of Fit Tests for Multivariate Normality