Compositional data for 464 clay minerals (2:1 type) were analyzed by statistical techniques. The objective was to understand the similarities and differences between the groups and subgroups and to evaluate statistically clay mineral classification in terms of chemical parameters. The statistical properties of the distributions of total layer charge (TLC), K, VIAl, VIMg, octahedral charge (OC) and tetrahedral charge (TC) were initially evaluated. Critical-difference (P = 1%) comparisons of individual characteristics show that all the clay micas (illite, glauconite and celadonite) differ significantly from all the smectites (montmorillonite, beidellite, nontronite and saponite) only in their TLC and K levels; they cannot be distinguished by their VIAl, VIMg, TC or OC values which reveal no significant differences between several minerals.

Linear discriminant analysis using equal prior was therefore performed to analyze the combined effect of all the chemical parameters. Using six parameters [TLC, K, VIAl, VIMg, TC and OC], eight minerals groups could be derived, corresponding to the three clay micas, four smectites (mentioned above) and vermiculite. The fit between predicted and experimental values was 88.1%. Discriminant analysis using two parameters (TLC and K) resulted in classification into three broad groups corresponding to the clay micas, smectites and vermiculites (87.7% fit). Further analysis using the remaining four parameters resulted in subgroup-level classification with an 85–95% fit between predicted and experimental results. The three analyses yielded D2 Mahalanobis distances, which quantify chemical similarities and differences between the broad groups, within members of a subgroup and also between the subgroups. Classification functions derived here can be used as an aid for classification of 2:1 minerals.

Knowledge on genetic architecture and inheritance of tomato shelf life contributing traits in different genetic backgrounds is a key issue for shelf life improvement. An investigation was undertaken to estimate the nature and magnitude of variability, traits inter-relationships, third and fourth degree statistics to unravel the genetics of 18 fruit quality and yield traits governing shelflife in F2 population of ‘Arka Vikas’ × ‘Red ball’ cross. The wider standardized range and higher estimates of phenotypic coefficient of variation indicated prevalence of adequate variability for fruit quality and yield traits. Fruit firmness and pericarp thickness ranged from 1.20–3.44 kg/cm2 and 2.44–5.31 mm respectively. Pulp content and shelflife ranged from 58.59–94.70% and 10.60–26.40 days respectively. Significant positive correlation with direct effect on fruit shelf life was exhibited by fruit firmness, pericarp thickness, TSS, titratable acidity, pulp content, fruit length and locule number. Positive skewness with platykurtic distribution recorded for TSS, lycopene, ascorbic acid, titratable acidity, fruit length, weight, pericarp thickness, plant height and number of branches. Negatively skewed with platykurtic distribution observed for pH, fruit diameter, firmness, pulp content, locule number, shelf life and number of clusters which signified duplicate epistasis of dominant genes in traits inheritance. The transgressive segregants for fruit quality traits indicated complementary effects of dispersed allele combinations between parents. Additive and dominance components could be exploited in the advanced segregating population by evaluating large number of families. In addition to additive effects, predominance of dominance effects of genes are important in inheritance of fruit quality traits governing shelflife.

This paper investigates the ordering properties of largest claim amounts in heterogeneous insurance portfolios in the sense of some transform orders, including the convex transform order and the star order. It is shown that the largest claim amount from a set of independent and heterogeneous exponential claims is more skewed than that from a set of independent and homogeneous exponential claims in the sense of the convex transform order. As a result, a lower bound for the coefficient of variation of the largest claim amount is established without any restrictions on the parameters of the distributions of claim severities. Furthermore, sufficient conditions are presented to compare the skewness of the largest claim amounts from two sets of independent multiple-outlier scaled claims according to the star order. Some comparison results are also developed for the multiple-outlier proportional hazard rates claims. Numerical examples are presented to illustrate these theoretical results.

This article examines the effects of ocean-related decadal climate variability (DCV) phenomena on climate and the effects of both climate shifts and independent DCV events on crop yields. We address three DCV phenomena: the Pacific Decadal Oscillation (PDO), the Tropical Atlantic Sea-Surface Temperature Gradient (TAG), and the Western Pacific Warm Pool (WPWP). We estimate the joint effect of these DCV phenomena on the mean, variance, and skewness of crop yield distributions. We found regionally differentiated impacts of DCV phenomena on growing degree days, precipitation, and extreme weather events, which in turn alter distributions of U.S. regional crop yields.

We determine the production risk effects and welfare implications of single-trait Bt corn adoption in the Philippines. We use a stochastic production function estimation approach that allows for examining the skewness effects of Bt within a damage abatement specification. Our results indicate that Bt corn has a statistically significant yield increasing, risk-increasing (i.e., variance-increasing) and downside risk-reducing (i.e., skewness-increasing) effects. Based on risk premium, certainty equivalent, and loss probability welfare measures, Bt corn farmers in the Philippines are better-off (in absolute terms) relative to non-Bt farmers given Bt corn's dominant yield increasing effect and downside risk-reducing effect.

Substitutive (replacement) and partial additive experimental designs, with their underlying models, remain the two most popular techniques in weed-crop competition studies, despite considerable criticism of these approaches in the recent literature. We review standard designs for two-species competition experiments and demonstrate the advantages of a reciprocal yield model applied to data from an additive series experiment, using mixtures of Japanese millet and tomato. A traditional replacement series analysis failed to provide a general model of competition among these two species over several total plant densities, while an application of a reciprocal yield (inverse linear) model to the same data was successful. This technique allows evaluation of the influences of both weed on crop and crop on weed, as well as the partitioning of net competition effects into intra- and interspecific components. One Japanese millet plant was competitively equivalent to 3.7 tomato plants, as measured by effects on tomato biomass, while one tomato plant was equivalent to 0.14 Japanese millet plants, as measured by effects on millet biomass. Skewness of per plant biomass distribution is shown to be a result but not an unambiguous measure of competition. Expansion of a reciprocal yield model to mixtures of more than two species is illustrated using three species of duckweed. While some caution is recommended, the reciprocal yield analysis applied to data from appropriately designed experiments is a substantial improvement over more traditional methods.

We study the properties of the multivariate skew normal distribution as an approximation to the distribution of the sum of n independent, identically distributed random vectors. More precisely, we establish conditions ensuring that the uniform distance between the two distribution functions converges to 0 at a rate of n-2/3. The advantage over the corresponding normal approximation is particularly relevant when the summands are skewed and n is small, as illustrated for the special case of exponentially distributed random variables. Applications to some well-known multivariate distributions are also discussed.

In this paper, we investigate the ability of a modified real business cycle (RBC) model to reproduce asymmetries observed for macroeconomic variables over the business cycle. To replicate the empirical skewness of major U.S. macroeconomic variables, we introduce a capacity constraint into an otherwise prototypical RBC model. This constraint emerges because of the assumption of kinked marginal costs of utilization, where the kink is located at a utilization rate of 100%. We find that a model with a suitably calibrated cost function reproduces the empirical coefficients of skewness remarkably well.