This dataset is part of a series of datasets, where batteries are continuously cycled with randomly generated current profiles. Reference charging and discharging cycles are also performed after a fixed interval of randomized usage to provide reference benchmarks for battery state of health. In this dataset, four 18650 Li-ion batteries (Identified as RW25, RW26, RW27 and RW28) were continuously operated by repeatedly charging them to 4.2V and then discharging them to 3.2V using a randomized sequence of discharging currents between 0.5A and 5A. This type of discharging profile is referred to here as random walk (RW) discharging. A customized probability distribution is used in this experiment to select a new load setpoint every 1 minute during RW discharging operation. The custom probability distribution was designed to be skewed towards selecting higher currents. The ambient temperature at which the batteries are cycled was held at approximately 40C for these experiments.

This dataset is part of a series of datasets, where batteries are continuously cycled with randomly generated current profiles. Reference charging and discharging cycles are also performed after a fixed interval of randomized usage to provide reference benchmarks for battery state of health. In this dataset, four 18650 Li-ion batteries (Identified as RW17, RW18, RW19 and RW20) were continuously operated by repeatedly charging them to 4.2V and then discharging them to 3.2V using a randomized sequence of discharging currents between 0.5A and 5A. This type of discharging profile is referred to here as random walk (RW) discharging. A customized probability distribution is used in this experiment to select a new load setpoint every 1 minute during RW discharging operation. The custom probability distribution was designed to be skewed towards selecting higher currents.

This database includes simulated data showing the accuracy of estimated probability distributions of project durations when limited data are available for the project activities. The base project networks are taken from PSPLIB. Then, various stochastic project networks are synthesized by changing the variability and skewness of project activity durations. Number of variables: 20 Number of cases/rows: 114240 Variable List: • Experiment ID: The ID of the experiment • Experiment for network: The ID of the experiment for each of the synthesized networks • Network ID: ID of the synthesized network • #Activities: Number of activities in the network, including start and finish activities • Variability: Variance of the activities in the network (this value can be either high, low, medium or rand, where rand shows a random combination of low, high and medium variance in the network activities.) • Skewness: Skewness of the activities in the network (Skewness can be either right, left, None or rand, where rand shows a random combination of right, left, and none skewed in the network activities)
• Fitted distribution type: Distribution type used to fit on sampled data • Sample size: Number of sampled data used for the experiment resembling limited data condition • Benchmark 10th percentile: 10th percentile of project duration in the benchmark stochastic project network • Benchmark 50th percentile: 50th project duration in the benchmark stochastic project network • Benchmark 90th percentile: 90th project duration in the benchmark stochastic project network • Benchmark mean: Mean project duration in the benchmark stochastic project network • Benchmark variance: Variance project duration in the benchmark stochastic project network • Experiment 10th percentile: 10th percentile of project duration distribution for the experiment • Experiment 50th percentile: 50th percentile of project duration distribution for the experiment • Experiment 90th percentile: 90th percentile of project duration distribution for the experiment • Experiment mean: Mean of project duration distribution for the experiment • Experiment variance: Variance of project duration distribution for the experiment • K-S: Kolmogorov–Smirnov test comparing benchmark distribution and project duration • distribution of the experiment • P_value: the P-value based on the distance calculated in the K-S test

Trade-offs are a fundamental concept in evolutionary biology because they are thought to explain much of nature’s biological diversity, from variation in life-histories to differences in metabolism. Despite the predicted importance of trade-offs, they are notoriously difficult to detect. Here we contribute to the existing rich theoretical literature on trade-offs by examining how the shape of the distribution of resources or metabolites acquired in an allocation pathway influences the strength of trade-offs between traits. We further explore how variation in resource distribution interacts with two aspects of pathway complexity (i.e., the number of branches and hierarchical structure) affects tradeoffs. We simulate variation in the shape of the distribution of a resource by sampling 106 individuals from a beta distribution with varying parameters to alter the resource shape. In a simple “Y-model” allocation of resources to two traits, any variation in a resource leads to slopes less than -1, with left skewed and symmetrical distributions leading to negative relationships between traits, and highly right skewed distributions associated with positive relationships between traits. Adding more branches further weakens negative and positive relationships between traits, and the hierarchical structure of pathways typically weakens relationships between traits, although in some contexts hierarchical complexity can strengthen positive relationships between traits. Our results further illuminate how variation in the acquisition and allocation of resources, and particularly the shape of a resource distribution and how it interacts with pathway complexity, makes it challenging to detect trade-offs. We offer several practical suggestions on how to detect trade-offs given these challenges. Methods Overview of Flux Simulations To study the strength and direction of trade-offs within a population, we developed a simulation of flux in a simple metabolic pathway, where a precursor metabolite emerging from node A may either be converted to metabolic products B1 or B2 (Fig. 1). This conception of a pathway is similar to De Jong and Van Noordwijk’s Y-model (Van Noordwijk & De Jong, 1986; De Jong & Van Noordwijk, 1992), but we used simulation instead of analytical statistical models to allow us to consider greater complexity in the distribution of variables and pathways. For a simple pathway (Fig. 1), the total flux Jtotal (i.e., the flux at node A, denoted as JA) for each individual (N = 106) was first sampled from a predetermined beta distribution as described below. The flux at node B1 (JB1) was then randomly sampled from this distribution with max = Jtotal = JA and min = 0. The flux at the remaining node, B2, was then simply the remaining flux (JB2 = JA - JB1). Simulations of more complex pathways followed the same basic approach as described above, with increased numbers of branches and hierarchical levels added to the pathway as described below under Question 2. The metabolic pathways were simulated using Python (v. 3.8.2) (Van Rossum & Drake Jr., 2009) where we could control the underlying distribution of metabolite allocation. The output flux at nodes B1 and B2 was plotted using R (v. 4.2.1) (Team, 2022) with the resulting trade-off visualized as a linear regression using the ggplot2 R package (v. 3.4.2) (Wickham, 2016). While we have conceptualized the pathway as the flux of metabolites, it could be thought of as any resource being allocated to different traits. Question 1: How does variation in resource distribution within a population affect the strength and direction of trade-offs? We first simulated the simplest scenario where all individuals had the same total flux Jtotal = 1, in which case the phenotypic trade-off is expected to be most easily detected. We then modified this initial scenario to explore how variation in the distribution of resource acquisition (Jtotal) affected the strength and direction of trade-offs. Specifically, the resource distribution was systematically varied by sampling n = 103 total flux levels from a beta distribution, which has two parameters alpha and beta that control the size and shape of the distribution (Miller & Miller, 1999). When alpha is large and beta is small, the distribution is left skewed, whereas for small alpha and large beta, the distribution is right skewed. Likewise, for alpha = beta, the curve is symmetrical and approximately normal when the parameters are sufficiently large (>2). We can thus systematically vary the underlying resource distribution of a population by iterating through values of alpha and beta from 0.5 to 5 (in increments of 0.5), which was done using the NumPy Python package (v. 1.19.1) (Harris et al., 2020). The resulting slope of each linear regression of the flux at B1 and B2 (i.e., the two branching nodes) was then calculated using the lm function in R and plotted as a contour map using the latticeExtra Rpackage (v. 0.6-30) (Sarkar, 2008). Question 2: How does the complexity of the pathway used to produce traits affect the strength and direction of trade-offs? Metabolic pathways are typically more complex than what is described above. Most pathways consist of multiple branch points and multiple hierarchical levels. To understand how complexity affects the ability to detect trade-offs when combined with variation in the distribution of total flux we systematically manipulated the number of branch points and hierarchical levels within pathways (Fig. 1). We first explored the effect of adding branches to the pathway from the same node, such that instead of only branching off to nodes B1 and B2, the pathway branched to nodes B1 through to Bn (Fig. 1B), where n is the total number of branches (maximum n = 10 branches). Flux at a node was calculated as previously described, and the remaining flux was evenly distributed amongst the remaining nodes (i.e., nodes B2 through to Bnwould each receive J2-n = (Jtotal - JB1)/(n - 1) flux). For each pathway, we simulated flux using a beta distribution of Jtotalwith alpha = 5, beta = 0.5 to simulate a left skewed distribution, alpha = beta = 5 to simulate a normal distribution, and with alpha = 0.5, beta = 5 to simulate a right skewed distribution, as well as the simplest case where all individuals have total flux Jtotal = 1. We next considered how adding hierarchical levels to a metabolic pathway affected trade-offs. We modified our initial pathway with node A branching to nodes B1 and B2, and then node B2 further branched to nodes C1 and C2 (Fig. 1C). To compute the flux at the two new nodes C1 and C2, we simply repeated the same calculation as before, but using the flux at node B2, JB2, as the total flux. That is, the flux at node C1 was obtained by randomly sampling from the distribution at B2 with max = JB and min = 0, and the flux at node C2 is the remaining flux (JC = JB2 - JC1). Much like in the previous scenario with multiple branch points, we used three beta distributions (with the same parameters as before) to represent left, normal, and right skewed resource distributions, as well as the simplest case where Jtotal = 1 for all individuals. Quantile Regressions We performed quantile regression to understand whether this approach could help to detect trade-offs. Quantile regression is a form of statistical analysis that fits a curve through upper or lower quantiles of the data to assess whether an independent variable potentially sets a lower or upper limit to a response variable (Cade et al., 1999). This type of analysis is particularly useful when it is thought that an independent variable places a constraint on a response variable, yet variation in the response variable is influenced by many additional factors that add “noise” to the data, making a simple bivariate relationship difficult to detect (Thomson et al., 1996). Quantile regression is an extension of ordinary least squares regression, which regresses the best fitting line through the 50th percentile of the data. In addition to performing ordinary least squares regression for each pairwise comparison between the four nodes (B1, B2, C1, C2), we performed a series of quantile regressions using the ggplot2 R package (v. 3.4.2), where only the qth quantile was used for the regression (q = 0.99 and 0.95 to 0.5 in increments of 0.05, see Fig. S1) (Cade et al., 1999).

Geographically Weighted Regression (GWR) has gained widespread popularity across various disciplines for investigating spatial heterogeneity with respect to data relationships in georeferenced datasets. However, GWR is typically limited to the analysis of continuous dependent variables, which are assumed to follow a symmetric normal distribution. In many fields, nonnegative continuous data are often observed and may contain substantial amounts of zeros followed by a right-skewed distribution of positive values. When dealing with such type of outcomes, GWR may not provide adequate insights into spatially varying regression relationships. This study intends to extend the GWR based on a compound Poisson distribution. Such an extension not only allows for exploration of relationship heterogeneity but also accommodates nonnegative continuous response variables. We provide a detailed specification of the proposed model and discuss related modeling issues. Through simulation experiments, we assess the performance of this novel approach. Finally, we present an empirical case study using a dataset on dengue fever in Tainan, Taiwan, to demonstrate the practical applicability and utility of our proposed methodology.

1. The performance of ectotherms integrated over time depends in part on the position and shape of the distribution of body temperatures (Tb) experienced during activity. For several complementary reasons, physiological ecologists have long expected that Tb distributions during activity should have a long left tail (left-skewed); but only infrequently have they quantified the magnitude and direction of Tb skewness in nature.
2. To evaluate whether left-skewed Tb distributions are general for diurnal desert lizards, we compiled and analyzed Tb (∑ = 9,023 temperatures) from our own prior studies of active desert lizards on three continents (25 species in Western Australia, 10 in the Kalahari Desert of Africa, and 10 species in western North America). We gathered these data over several decades, using standardized techniques.
3. Many species showed significantly left-skewed Tb distributions, even when records were restricted to summer months. However, magnitudes of skewness were always small, such that mean Tb were never more than 1°C lower than median Tb. The significance of Tb skewness was sensitive to sample size, and power tests reinforced this sensitivity.
4. The magnitude of skewness was not obviously related to phylogeny, desert, body size, or median body temperature. Moreover, formal phylogenetic analysis is inappropriate because geography and phylogeny are confounded (that is, are highly collinear).
5. Skewness might be limited if lizards pre-warm inside retreats before emerging in the morning, emerge only when operative temperatures are high enough to speed warming to activity Tb, or if cold lizards are especially wary and difficult to spot or catch. Telemetry studies may help evaluate these possibilities.

Raw data for Figure 5

Raw data for figures 3 and 4

Abstract: Employee attitude surveys are important tools for organizational development. To gain insights into employees’ attitudes, surveys most often use Likert-type items. Measures assessing these attitudes frequently use intensifiers (e.g., extremely, very) in item stems. To date little is known about the effects of intensifiers in the item stem on response behavior. They are frequently used inconsistently, which potentially has implications for the comparability of results in the context of benchmarking. Also, results often suffer from left-skewed distributions limiting data quality for which the use of intensifiers potentially offers a remedy. Therefore, we systematically examine the effects of intensifiers’ on response behavior in employee attitude surveys and their potential to remedy the issue of left-skewed distributions. In three studies, we assess effects on level, skewness and nomological structure. Study 1 examines the effects of intensifier strength in the item stem, while Studies 2 and 3 assess whether intensifier salience would increase these effects further. Interestingly, results did not show systematic effects. Future research ideas in regards to item design and processing as well as practical implications for the design of employee attitude surveys are discussed. Other: Does “very” make a difference? Effects of intensifiers in item stems of employee attitude surveys on response behavior - in preparation

In this paper we model Value-at-Risk (VaR) for daily asset returns using a collection of parametric univariate and multivariate models of the ARCH class based on the skewed Student distribution. We show that models that rely on a symmetric density distribution for the error term underperform with respect to skewed density models when the left and right tails of the distribution of returns must be modelled. Thus, VaR for traders having both long and short positions is not adequately modelled using usual normal or Student distributions. We suggest using an APARCH model based on the skewed Student distribution (combined with a time-varying correlation in the multivariate case) to fully take into account the fat left and right tails of the returns distribution. This allows for an adequate modelling of large returns defined on long and short trading positions. The performances of the univariate models are assessed on daily data for three international stock indexes and three US stocks of the Dow Jones index. In a second application, we consider a portfolio of three US stocks and model its long and short VaR using a multivariate skewed Student density.

Geographically Weighted Regression (GWR) has gained widespread popularity across various disciplines for investigating spatial heterogeneity with respect to data relationships in georeferenced datasets. However, GWR is typically limited to the analysis of continuous dependent variables, which are assumed to follow a symmetric normal distribution. In many fields, nonnegative continuous data are often observed and may contain substantial amounts of zeros followed by a right-skewed distribution of positive values. When dealing with such type of outcomes, GWR may not provide adequate insights into spatially varying regression relationships. This study intends to extend the GWR based on a compound Poisson distribution. Such an extension not only allows for exploration of relationship heterogeneity but also accommodates nonnegative continuous response variables. We provide a detailed specification of the proposed model and discuss related modeling issues. Through simulation experiments, we assess the performance of this novel approach. Finally, we present an empirical case study using a dataset on dengue fever in Tainan, Taiwan, to demonstrate the practical applicability and utility of our proposed methodology.

Random asymmetry, that is the co-existence of left- and right-sided (or -handed) individuals within a population, is a particular case of natural variation; what triggers and maintains such dimorphisms remains unknown in most cases. Here, we report a field-based cage experiment in the scale-eating Tanganyikan cichlid Perissodus microlepis (Boulenger, 1898), which occurs in two morphs in nature: left-skewed and right-skewed individuals with respect to mouth orientation. Using underwater cages stocked with scale-eaters and natural prey fish, we first confirm that, under semi-natural conditions, left-skewed scale-eaters preferentially attack the right flank of their prey, whereas right-skewed individuals feed predominantly from the left side. We then demonstrate that scale-eaters have a higher probability for successful attacks when kept in dimorphic experimental populations (left- AND right-skewed morphs together) as compared to monomorphic populations (left- OR right-skewed morphs), most likely because prey fishes fail to accustom to strikes from both sides. The significantly increased probability for attacks appears to be the selective agent responsible for the evolution and maintenance of mouth dimorphism in P. microlepis, lending further support to the hypothesis that negative frequency-dependent selection is the stabilizing force balancing the mouth dimorphism at quasi-equal ratios in scale-eating cichlids.

Data and replication information for "Uncertainty, skewness, and the business cycle through the MIDAS lens" by Efrem Castelnuovo and Lorenzo Mori; published in Journal of Applied Econometrics, 2024. We employ a mixed-frequency quantile regression approach to model the time-varying conditional distribution of the US real GDP growth rate. We show that monthly information on financial conditions improves the predictive power of an otherwise quarterly-only model. We combine selected quantiles of the estimated conditional distribution to produce novel measures of uncertainty and skewness. Embedding these measures in a VAR framework, we show that unexpected changes in uncertainty are associated with an increase in (left) skewness and a downturn in real activity. Business cycle effects are significantly downplayed if we consider a quarterly-only quantile regression model. We find the endogenous response of skewness to substantially amplify the recessionary effects of uncertainty shocks. Finally, we construct a monthly-frequency version of our uncertainty measure and document the robustness of our findings.

Over the past 35 years there has been a near doubling in the worldwide prevalence of obesity. Body Mass Index (BMI) distributions in high-income societies have increasingly shifted rightwards, corresponding to increases in average BMI that are due to well-studied changes in the socioeconomic environment. However, in addition to this shift, BMI distributions have also shown marked changes in their particular shape over time, exhibiting an ongoing right-skewed broadening that is not well understood. Here, we compile and analyze the largest data set so far of year-over-year BMI changes. The data confirm that, on average, heavy individuals become lighter while light individuals become heavier year-over-year, and also show that year-over-year BMI evolution is characterized by fluctuations with a magnitude that is linearly proportional to BMI. We find that the distribution of human BMIs is intrinsically dynamic—due to the short-term variability of human weight—and its shape is determined by a balance between deterministic drift towards a natural set point and diffusion resulting from random fluctuations in, e.g., diet and physical activity. We formulate a stochastic mathematical model for BMI dynamics, deriving a theoretical shape for the BMI distribution and offering a mechanism that may explain the right-skewed broadening of BMI distributions over time. An extension of the base model investigates the hypothesis that peer-to-peer social influence plays a role in BMI dynamics. While including this effect improves the fit with the data, indicating that correlations in the behavior of individuals with similar BMI may be important for BMI dynamics, testing social transmission against other plausible unmodeled effects and interpretations remains the subject of future work. Implications of our findings on the dynamics of BMI distributions for public health interventions are discussed.

Definition: The skewness "Sk1" is a measure of the symmetry of the cumulative curve, which indicates the ratio of coarse to fine parts in the particle size distribution. Folk & Ward (1957) quantify this symmetry in a value range from -1 to 1. Positive values ​​greater than 0 to 1 indicate a "left skewing" for metric cumulative curves, i.e. fine grain fractions predominate in comparison to coarse fractions. Negative values ​​of less than 0 to -1 indicate a "right-skewing" for metric cumulative curves, which correspondingly indicates a predominance of coarse compared to fine fractions. Sk1 = 0 indicates a perfectly symmetrical cumulative curve. Conclusions about the deposition environment can be drawn from the skewness. Data generation: The basis for sedimentological evaluations are surface sediment samples, which were interpolated within the framework of the EasyGSH project using anisotropic interpolation methods and taking into account hydrodynamic factors and erosion and sedimentation processes from individual samples from different years to a grid valid for one year. The sediment distribution is therefore available as a cumulative curve at each of these grid nodes. For the German Bight, this basic product is available for the years 1996, 2006 and 2016 in a 100 m grid, for the exclusive economic zone of Germany for the year 1996 in a 250 m grid. The parts for ϕ5, ϕ16, ϕ50, ϕ84 and ϕ95 required for the calculation rule for the skewness according to Folk & Ward (1957) can be determined directly from these cumulative curves and the skewness parameter Sk1 can be calculated. Product: 100 m grid of the German Bight (1996, 2006, 2016) or 250 m grid of the Exclusive Economic Zone (1996), on which the skewness Sk1 according to Folk & Ward (1957) is stored at each grid node. The product is provided in GeoTiff format. Literature: Folk, R.L., & Ward, W.C. (1957). A study in the significance of grain size parameters. Journal of Petrology, 37, 327-354. For further information, please refer to the information portal (http://easygsh.wb.tu-harburg.de/) and the download portal (https://mdi-de.baw.de/easygsh/). English Download: The data for download can be found under References ("further references"), where the data can be downloaded directly or via the web page redirection to the EasyGSH-DB portal. For further information, please refer to the download portal (https://mdi-de.baw.de/easygsh/EasyEN_index.html).

1. Parents often face an investment trade-off between either producing many small or fewer large offspring. When environments vary predictably, the fittest parental solution matches available resources by varying only number of offspring and never optimal individual size. However when mismatches occur often between parental expectations and true resource levels, dynamic models like multifaceted parental investment (MFPI) and parental optimism (PO) both predict offspring size can vary significantly. MFPI is a “realist” strategy: parents assume future environments of average richness. When resources exceed expectations and it is too late to add more offspring, the best-case solution increases investment per individual. Brood size distributions therefore track the degree of mismatch from right-skewed around an optimal size (slight underestimation of resources), to left-skewed around a maximal size (gross underestimation). Conversely, PO is an “optimist” strategy: parents assume maximally good resource futures and match numbers to that situation. Normal or lean years do not affect “core” brood as costs primarily fall on excess “marginal” siblings who die or experience stunted growth (producing left-skewed distributions). 2. Investment patterns supportive of both MFPI and PO models have been observed in nature, but studies that directly manipulate food resources in order to test predictions are lacking. Ant colonies produce many offspring per reproductive cycle, and are amenable to experimental manipulation in ways that can differentiate between MFPI and PO investment strategies. 3. Colonies in a natural population of a harvester ant (Pogonomymex salinus) were protein-supplemented over two years and mature sexual offspring were collected annually prior to their nuptial flight. 4. Several results support either MFPI or PO in terms of patterns in offspring size distributions and how protein differentially affected male and female production. Unpredicted by either model, however, is that supplementation affected distributions more strongly across years than within (e.g., small females are significantly rarer in the year after colonies receive protein). 5. Parental investment strategies in P. salinus vary dynamically across years and conditions. Finding that past conditions can more strongly affect reproductive decisions than current ones, however, is not addressed by models of parental investment.

This paper proposes a conditional density model that allows for differing left/right tail indices and time-varying volatility based on the dynamic conditional score (DCS) approach. The asymptotic properties of the maximum likelihood estimates are presented under verifiable conditions together with simulations showing effective estimation with practical sample sizes. It is shown that tail asymmetry is prevalent in global equity index returns and can be mistaken for skewness through the center of the distribution. The importance of tail asymmetry for asset allocation and risk premia is demonstrated in-sample. Application to portfolio construction out-of-sample is then considered, with a representative investor willing to pay economically and statistically significant management fees to use the new model instead of traditional skewed models to determine their asset allocation.

Chloride concentration (in mg/litre) in water data. [30].

Age-sex charts emphasize the gap between the numbers of males and females at a specific age group. It also illustrates the age and gender trends across all age and gender groupings. A chart skewed heavily to the left describes a very young population while a chart skewed heavily to the right illustrates an aging population.

1. Animal group size distributions are often right-skewed, whereby most groups are small, but most individuals occur in larger groups that may also disproportionately affect ecology and policy. In this case, examining covariates associated with upper quantiles of the group size distribution could facilitate better understanding and management of large animal groups. 2. We studied wintering elk groups in Wyoming, where group sizes span several orders of magnitude, and issues of disease, predation and property damage are affected by larger group sizes. We used quantile regression to evaluate relationships between the group size distribution and variables of land use, habitat, elk density and wolf abundance to identify conditions important to larger elk groups. 3. We recorded 1263 groups ranging from 1 to 1952 elk and found that across all quantiles of group size, group sizes were larger in open habitat and on private land, but the largest effect occurred between irrigated and non-irrigated land [e.g. the 90th quantile group size increased by 135 elk (95% CI = 42, 227) on irrigation]. 4. Only upper quantile group sizes were positively related to broad-scale measures of elk density and wolf abundance. For wolf abundance, this effect was greater on elk groups found in open habitats and private land than those in closed habitats or public land. If we had limited our analysis to mean or median group sizes, we would not have detected these effects. 5. Synthesis and applications. Our analysis of elk group size distributions using quantile regression suggests that private land, irrigation, open habitat, elk density and wolf abundance can affect large elk group sizes. Thus, to manage larger groups by removal or dispersal of individuals, we recommend incentivizing hunting on private land (particularly if irrigated) during the regular and late hunting seasons, promoting tolerance of wolves on private land (if elk aggregate in these areas to avoid wolves) and creating more winter range and varied habitats. Relationships to the variables of interest also differed by quantile, highlighting the importance of using quantile regression to examine response variables more completely to uncover relationships important to conservation and management.