Mapping of Beta Distribution for the Study of Dispersed Materials

In the study of polydisperse materials, most of the experimental particle size distributions were obtained on bounded intervals. In these cases, it is also desirable to use bounded models with different shapes to simulate the results of studying polydisperse and powder materials. The beta distribution is often used to approximate results due to the fact that this distribution contains many forms for displaying realizations on a limited interval. With the development of computer technology, there has been an increased interest in the use of beta distribution in the modern practice of analyzing results. Meanwhile, there remains a limitation in the use of the beta distribution that is associated with the choice of distribution shape. The possibilities of using known shape measures for mapping beta distribution in this paper is discusses. On the example of the space of shape measure of kurtosis and skewness, the limited use of only probabilistic measures of shapes is illustrated. It is proposed to use the entropy coefficients as an additional informational parameter of the beta distribution shape. On the base of a features comparison of the entropy coefficients for biased and unbiased beta distributions, recommendations for their application are given. By using the example of beta distributions mapping in the space of asymmetry and the entropy coefficient, it is shown that the synergistic combination of probabilistic and informational measures of the shape allows expanding the possibilities of estimating the shape parameters beta distributions. Two methods to display the positions of realizations of beta distributions is proposed. There are trajectories on a constant ratio of shape and realizations position curve on equal values of one parameter. In particular, the features of the choice of beta distributions with negative skewness are discussed.

Heritability and Genetic Advance as Genetic Indicators for Improvement in Two Cotton Crosses

The primary breeding goal for the Egyptian cotton breeding program is how to genetically improve both yield and fibre quality traits, while most of these agronomically traits are biometric traits. The objective of the present study is to evaluate variability and estimate frequency of transgressive segregants in order to isolate early superior individual plants which exceeding the better parent for some yield and fiber quality traits in two intraspecific cotton crosses in early transgressive segregating generation (F2 ). The F1 was highly significant superior than the better parent (Giza 97 and Giza 94) of the two crosses for all the studied traits except boll weight and lint %. Most of the studied traits in F2 generation showed high values of broad sense heritability coupled with low GAM % indicated that these traits controlled by non-additive gene action. All the studied traits had positive skewness sign except for lint %. Presley index and uniformity index for the two cotton crosses and upper half mean for cross II showed negative skewness. The negative skewness indicated that the population had more plants frequency with higher mean values than population mean and controlled by dominancy alleles. While, the traits that had positive skewness are controlled by additive gene action. The two cotton crosses showed transgressive segregants for all the studied traits. Cross I has higher transgressive index for yield traits than cross II, while cross II has the same trend for fiber quality traits than cross I. These results indicated that the both parents of the two cotton crosses had different alleles and genes governing the respective studied traits, which will help cotton breeder to combine beneficial alleles into a single genotype by rigorous selection process. This strategy could be used to improve many economic biometric traits by using better and stringent selection procedure to enhance Egyptian cotton productivity which is major concern in Egypt. The breeder can use transgressive segregation as an indicator of genetic variability to select the most superior plants.

Influence of Particle Distribution on Macroscopic Properties of Particle Flow Model

The particle flow discrete element models for uniaxial compression and tensile tests of rocks are established to study the influence of the particle distribution randomness on the macroscopic mechanical properties of such model. The results of macroscopic mechanical properties show strong discreteness due to the variance of particle distributions, in which compressive strength, tensile strength and Poisson's ratio follow the normal distribution and the Young's modulus follows the negative skewness distribution. The average values of the macroscopic strength obtained based on multiple calculations with different particle distributions should be used for the calibration of microscopic parameters. According to the relationship between sample size and deviation of macro strength averages, the minimum calculation number required to obtain high-precision macro strength with different confidence levels is given.

Homogeneous and heterogeneous propagation of COVID-19 from super-spreading to super-isolation

We investigated daily COVID-19 cases and death in the 337 lower tier local authority regions in England and Wales to better understand how the disease propagated over a 10-month period. Population density scaling models revealed residual variance and skewness to be sensitive indicators of the dynamics of propagation. Lockdowns and schools reopening triggered increased variance indicative of outbreaks with local impact and country scale heterogeneity. University reopening and December holidays triggered reduced variance indicative of country scale homogenisation which reached a minimum after New Year. Homogeneous propagation was associated with better correspondence with normally distributed residuals while heterogeneous propagation was more consistent with skewed models. Skewness varied from strongly negative to strongly positive revealing an unappreciated feature of community propagation. Hot spots and super-spreading events are well understood descriptors of regional disease dynamics that would be expected to be associated with positively skewed distributions. Positively skewed behaviour was observed; however, negative skewness indicative of “cold-spots” and “super-isolation” dominated for approximately 4 months during the period of study. In contrast, death metrics showed near constant behaviour in scaling, variance, and skewness metrics over the full period with rural regions preferentially affected, an observation consistent with regional age demographics in England and Wales.

A CT radiomics analysis of COVID-19-related ground-glass opacities and consolidation: Is it valuable in a differential diagnosis with other atypical pneumonias?

Purpose To evaluate the discrimination of parenchymal lesions between COVID-19 and other atypical pneumonia (AP) by using only radiomics features. Methods In this retrospective study, 301 pneumonic lesions (150 ground-glass opacity [GGO], 52 crazy paving [CP], 99 consolidation) obtained from nonenhanced thorax CT scans of 74 AP (46 male and 28 female; 48.25±13.67 years) and 60 COVID-19 (39 male and 21 female; 48.01±20.38 years) patients were segmented manually by two independent radiologists, and Location, Size, Shape, and First- and Second-order radiomics features were calculated. Results Multiple parameters showed significant differences between AP and COVID-19-related GGOs and consolidations, although only the Range parameter was significantly different for CPs. Models developed by using the Bayesian information criterion (BIC) for the whole group of GGO and consolidation lesions predicted COVID-19 consolidation and AP GGO lesions with low accuracy (46.1% and 60.8%, respectively). Thus, instead of subjective classification, lesions were reclassified according to their skewness into positive skewness group (PSG, 78 AP and 71 COVID-19 lesions) and negative skewness group (NSG, 56 AP and 44 COVID-19 lesions), and group-specific models were created. The best AUC, accuracy, sensitivity, and specificity were respectively 0.774, 75.8%, 74.6%, and 76.9% among the PSG models and 0.907, 83%, 79.5%, and 85.7% for the NSG models. The best PSG model was also better at predicting NSG lesions smaller than 3 mL. Using an algorithm, 80% of COVID-19 and 81.1% of AP patients were correctly predicted. Conclusion During periods of increasing AP, radiomics parameters may provide valuable data for the differential diagnosis of COVID-19.

Buy-Side Competition and Momentum Profits

We show that a new measure of buy-side competition explains momentum profits. The momentum quintile spread is 1.11% when competition is low and negligible when competition is high. Better alphas are attained with superior Sharpe and Sortino ratios, with no negative skewness, and in more investible strategies featuring value-weighted portfolios and large capitalization stocks. Stock characteristics traditionally related to momentum do not explain our results. Tests based on long-term reversals, the trading patterns of funds, their style peers, distant funds, and retail investors suggest that slow information diffusion explains the large momentum spreads and momentum reversals in low competition markets.

What Do Data on Millions of U.S. Workers Reveal About Lifecycle Earnings Dynamics?

We study individual male earnings dynamics over the life cycle using panel data on millions of U.S. workers. Using nonparametric methods, we first show that the distribution of earnings changes exhibits substantial deviations from lognormality, such as negative skewness and very high kurtosis. Further, the extent of these nonnormalities varies significantly with age and earnings level, peaking around age 50 and between the 70th and 90th percentiles of the earnings distribution. Second, we estimate nonparametric impulse response functions and find important asymmetries: Positive changes for high‐income individuals are quite transitory, whereas negative ones are very persistent; the opposite is true for low‐income individuals. Third, we turn to long‐run outcomes and find substantial heterogeneity in the cumulative growth rates of earnings and the total number of years individuals spend nonemployed between ages 25 and 55. Finally, by targeting these rich sets of moments, we estimate stochastic processes for earnings that range from the simple to the complex. Our preferred specification features normal mixture innovations to both persistent and transitory components and includes state‐dependent long‐term nonemployment shocks with a realization probability that varies with age and earnings.

Determination of the Order of Kinetics of a DTA Curve by Using the Concept of Skewness

In the present paper, a novel way of finding out the order of kinetics of differential thermal analysis (DTA) curves by using the concept of skewness (Sk) has been investigated. It is found that for a particular DTA peak, skewness is a function of both the order of kinetics and the quantity, First order DTA peaks are characterized by negative skewness whereas those for the second order are characterized by positive skewness. Therefore, skewness can be used as an indicator of the order of kinetics of a DTA peak. We have evaluated and compared the orders of kinetics of some reported DTA peaks using the concept of skewness and found that the resulting values of the orders of kinetics are in fair agreement with those reported in literature.

Forecasting VIX Using Filtered Historical Simulation*

We propose a new VIX forecast method using Generalized Autoregressive Conditional Heteroscedasticity models based on the filtered historical simulation put forward in Barone-Adesi, Engle, and Mancini (2008). The flexible change of measure accommodates for non-normalities such as negative skewness and positive excess kurtosis. We present an application for four well-established volatility indices (VIX9D, VIX, VIX3M, and VIX6M). Our results show that our proposed estimation method outperforms the Normal-VIX model of Hao and Zhang (2013) both in-sample and out-of-sample. Furthermore, the use of volatility indices reduces the computational burden significantly compared to the options-based pricing method.

Optimistically biased economic growth forecasts and negatively skewed annual variation

Authoritative economic growth forecasts are often optimistically biased. Negatively skewed variation--negative shocks being larger than positive shocks--could contribute to bias by making long-run average growth smaller than typical-year (median) growth. This positively biases forecasts based on typical years. We compare medians and means in real per-capita GDP growth across countries, regions, and time windows from 1820-2016. Over decadal periods, we find mean growth rates <1%/y smaller than median growth rates in most countries and regions (median 0.23%/y across countries). Surprisingly, we find both large- and medium-magnitude shocks contribute to these differences, rather than only large ‘black swan’ events. We find negative skewness correlated with high levels and slow growth of per-capita GDP and population, and high per-capita GDP growth volatility, building on previous studies. We find negative skewness alone insufficient to explain recent growth over-projections by the International Monetary Fund (IMF) and the U.S. Congressional Budget Office (CBO).