Measures Of Skewness Research Articles

Uncertainty, Skewness, and the Business Cycle Through the MIDAS Lens

ABSTRACTWe 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.

Indicators of sarcopenia and purpose in life levels in older adults: the influence of sociodemographic factors

This study aimed to compare the indicators of sarcopenia and the level of purpose in life among older adults, considering sociodemographic factors. It is a quantitative, analytical, observational, and cross-sectional study conducted with 128 older adults (≥60 years old) of both sexes residing in Brazil's Midwest and South regions. The study employed a unique methodology, including a sociodemographic questionnaire, the Purpose in Life Scale, and the SARC-f, which were administered to the participants. Data collection took place online from January 2024 to April 2024. The study's data analysis included the Kolmogorov-Smirnov test, measures of skewness and kurtosis, bootstrapping procedures, independent t-test, one-way ANOVA, and Tukey's post-hoc test, with a significance level of p < 0.05. The older adults showed a low risk of sarcopenia (1.23±1.97) and a moderate level of purpose in life (3.77± 0.63). Younger older adults (p = 0.005), those with completed higher education (p = 0.018), and those with higher income (p = 0.007) had a lower risk of sarcopenia. Younger older adults (p = 0.035) and those with higher incomes (p = 0.007) also had higher levels of purpose in life. Purpose in life showed a significant negative weak correlation with age (r = -0.24) and sarcopenia risk (r = -0.33) (p < 0.05). In conclusion, younger older adults and those with higher monthly incomes demonstrated a lower risk of sarcopenia and a higher level of purpose in life.

The Study of Segregation and its Consequences in the Kabul City

This study investigates urban segregation in Kabul, the capital of Afghanistan, utilizing a multifaceted theoretical framework that integrates various explanatory models of segregation. The research targets the general population of Kabul, with a sample size of 233 individuals selected through a non-probabilistic cluster sampling technique. Data were collected using a comprehensive questionnaire focused on the Afghan context, incorporating insights from relevant studies. The analysis was conducted using SPSS software, employing both descriptive and inferential statistical methods. Demographic characteristics and participant responses in ethnically dominated areas were summarized using frequencies and percentages, while key variables were examined using measures of central tendency, dispersion, and distribution, including mean, standard deviation, variance, skewness, and kurtosis. The segregation tendencies of Kabul residents were analyzed using T-test, ANOVA and Spearman correlation. The results reveal a pronounced level of segregation within Kabul, with significant implications including the reinforcement of ethnocentric attitudes, the preservation of distinct subcultural identities, enhanced feelings of community security, and increased intra-group political and social engagement. The study found that followers of Shia Islam tend to segregate themselves from other religious groups, while the Pashtun ethnic group shows the lowest tendency toward segregation. Additionally, Kabul citizens tend to live among their own religious groups and the lower the level of education of individuals, the greater their tendency to separation.

Evaluation of Community Pharmacist’s Knowledge, Attitudes, and Practices Regarding the Pharmacotherapy Management of Gouty Arthritis in Lahore, Pakistan

Background: Gouty arthritis is a prevalent but frequently misdiagnosed condition particularly in developing countries. As a medical expert pharmacists are essential to patient medication management, patient education, and treatment protocol adherence but insufficient information is present on related to gouty arthritis in Pakistan. Objective: The purpose of the study is to evaluate retail pharmacists (KAP) knowledge, attitude, practices regarding gouty arthritis in Lahore community pharmacies. It also examines the relationship between KAP scores and demographic characteristics finding gaps in pharmacist knowledge and treatment of arthritis. Methods: A study with a cross-sectional design was carried out on retail pharmacists working in community pharmacies throughout Lahore. Data on their knowledge attitude and practice regarding gouty arthritis were gathered using a structured questionnaire. The data were summarized using descriptive statistics. The Kolmogorov-Smirnov test evaluated normality, in addition to measures of skewness and kurtosis. Statistical analysis involved Fishers exact test and the Chi-square test to ascertain relationships between KAP scores and demographic factors. Effect size was measured using Cramer's V and Phi-square. Results: There is no significant association between demographics of pharmacists and knowledge. There is no association between our study variables and attitude. The post-hoc comparison of p values of different demographics shows no association with the practice regarding gouty arthritis. Conclusion: Despite their generally positive attitudes toward patient care community pharmacists have a notable knowledge gap regarding gouty arthritis. Enhanced training and education are required to improve community pharmacies handling of gout. Limitation such as sample size and response bias should be addressed in future research.

Multivariate process capability analysis for evaluating metal additive manufacturing via electron beam melting

Abstract Electron beam melting (EBM) as one of the relatively new metal AM techniques showed promising and increasing applications. Therefore, there is a need to evaluate the quality of the EBM process using its critical quality characteristics. However, EBM and different AM process parts have many functionally or statistically correlated quality characteristics. Consequently, the quality characteristics of the EBM process should be evaluated together. Therefore, this research aims to evaluate the quality of the EBM process using a multivariate process capability index (MPCI). In this study, the dimensional accuracy in different directions is considered as a quality characteristics. The proposed methodology involves producing a large sample of small specimens of square shape using EBM technology. Three critical dimensions of the specimen in the X, Y, and Z axis are investigated as quality characteristics. The dimensions of quality characteristics are measured using a precise measurement device. The normality and stability assumptions of the collected data are investigated using skewness measure, and multivariate process control chart respectively. Then a large sample of the multivariate normal data is simulated using computer software to estimate the percent of nonconforming (PNC) from the established specification limits, which is used to estimate MPCI. Finally, the capable tolerance of the process is estimated and the sensitivity analysis of variation is investigated. The results show the capability of the EBM process under different specification limits designations. Estimating MPCI revealed that the EBM process is capable under very coarse limits only. Moreover, the sensitivity analysis showed that variation in quality characteristics data is very sensitive for MPCI estimation, especially variation in width quality characteristic.

A new approach based on 2D wavelet transform in the analysis of wettability behavior and evaporation rate for the surface of PTFE dielectric material used in high voltage applications

In this study, a new approach based on 2D wavelet transform is proposed for the analysis of wettability behavior and evaporation rate. Droplet images were taken from the PTFE dielectric sample surface at 30th, 270th, 510th, 750th, 990th, 1230th, 1470th, and 1710th seconds. The droplet images were decomposed into sub-bands using functions from six different wavelet families. The energy, entropy, mean, standard deviation, skewness, and kurtosis measures were calculated using wavelet coefficients for each sub-band image. Linear, exponential, and polynomial fitting methods were used to estimate the contact angle of the droplet images. The energy and standard deviation values, which are the selected optimal measures, were used as input in the fitting methods, and the regression coefficient (R2) and Root Mean Square Error (RMSE) values of the fitting methods were calculated. Thus, a high-performing contact angle prediction model with 2nd level sub-band image wavelet coefficients has been obtained.

Nominal price illusion, return skewness, and momentum

We document a significantly negative association between the nominal price measure of Birru and Wang (2015) and the profit of the stock momentum strategy. The negative relationship is driven by the underperformance of loser stocks with high nominal price illusions. Further analysis shows that the previously documented positive correlations between return skewness measures and momentum profit are subsumed by the effect of nominal price on momentum profit.

Real-time forward-looking skewness over the business cycle

This paper measures option-implied skewness for individual firms and the S&P 500 index between 1980 and 2021, giving real-time measures of conditional micro and macro skewness. There are three key results: 1. Micro skewness is significantly procyclical, while macro skewness is acyclical; 2. Micro skewness leads the business cycle and is strongly linked to credit spreads, suggesting one potential causal channel; 3. Micro skewness is significantly, and not mechanically, correlated with macro volatility, implying that there is a common shock driving them both, which is also linked to the business cycle.

Implied volatility slopes and jumps in bitcoin options market

This paper derives a theoretical relation between the left and right slopes of the implied volatility curve with negative and positive price jumps. Empirical analysis using bitcoin options tick-by-tick data from Deribit exchange supported the theoretical findings that negative and positive jumps have reversal impacts on bitcoin options' implied volatility slopes even after the control of net-buying-pressure and realized positive and negative skewness measures.

Multivariate unified skew-[formula omitted] distributions and their properties

The unified skew-t (SUT) is a flexible parametric multivariate distribution that accounts for skewness and heavy tails in the data. A few of its properties can be found scattered in the literature or in a parameterization that does not follow the original one for unified skew-normal (SUN) distributions, yet a systematic study is lacking. In this work, explicit properties of the multivariate SUT distribution are presented, such as its stochastic representations, moments, SUN-scale mixture representation, linear transformation, additivity, marginal distribution, canonical form, quadratic form, conditional distribution, change of latent dimensions, Mardia measures of multivariate skewness and kurtosis, and non-identifiability issue. These results are given in a parameterization that reduces to the original SUN distribution as a sub-model, hence facilitating the use of the SUT for applications. Several models based on the SUT distribution are provided for illustration.

Estimation of a Measure of Skewness Taking the Median as the Axis of Symmetry

Estimation of a Measure of Skewness Taking the Median as the Axis of Symmetry

Measures of kurtosis: inadmissible for asymmetric distributions?

AbstractSkewness and kurtosis are natural characteristics of a distribution. While it has long been recognized that they are more intrinsically entangled than other characteristics like location and dispersion, this has recently been made more explicit by Eberl and Klar (Stat Papers 65:415–433, 2024) with regard to orders of kurtosis. In this paper, we analyze the implications of this entanglement on kurtosis measures in general and for several specific examples. As a key finding, we show that kurtosis measures that are defined in the classical order-based way, which is analogous to measures of location, dispersion and skewness, do not exist. This raises serious doubts about the frequent application of such measures to skewed data. We then consider old and new proposals for kurtosis measures and evaluate under which additional conditions they measure kurtosis in a meaningful way. Some measures also allow more specific representations of the influence of skewness on the measurement of kurtosis than are available in a general setting. This works particularly well for a family of newly introduced density-based kurtosis measures.

Lottery demand, weather and the cross-section of stock returns

We investigate the role that weather-induced mood plays in underperformance of lottery stocks. We hypothesize that during pleasant weather conditions, investors are more likely to become risk-taking and optimistic, and invest more in lottery stocks. This results in overpricing and lower expected return for these stocks. We use sky cloud cover as a proxy for the weather condition and show that the MAX effect mainly exists following sunny weather; however, there is less evidence for the MAX anomaly following cloudy weather. Our finding is robust to using alternative constructions of MAX and skewness measures as well as other proxies for weather condition such as rain, wind and temperature.

Sampling sufficiency to estimate the mean productive traits of buckwheat

The objective of this work was to determine the sample size (number of plants) necessary to estimate the mean productive traits of buckwheat (Fagopyrum esculentum), cultivars IPR91-Baili and IPR92-Altar, in the vegetative and flowering stages of the crop. Twenty-one uniformity trials were conducted for each cultivar (IPR91-Baili and IPR92-Altar). Six productive traits (leaf fresh matter, stem fresh matter, shoot fresh matter, leaf dry matter, stem dry matter and shoot dry matter) were evaluated in 2280 plants of each cultivar (IPR91-Baili and IPR92-Altar). Kolmogorov-Smirnov normality test was performed. Measures of central tendency, variability and skewness and were calculated. The sample size was calculated to estimate the mean for six traits, with estimation errors (semi-amplitudes of the 95% confidence interval) equal to 5%, 10%, 15% and 20% of the mean. There is variability in sample size between productive traits, cultivars and phenological stages of buckwheat. In an experiment to estimate the mean of these six traits of buckwheat, cultivars IPR91-Baili and IPR92-Altar, in the vegetative and flowering stages, with a maximum error of 20% of the mean at a 95% confidence interval, 80 plants per treatment are needed.

A Double Truncated Binomial Model to Assess Psychiatric Health through Brief Psychiatric Rating Scale: When is Intervention Useful?

A double truncated binomial distribution model with ‘u’ classes truncated on left and ‘v’ classes truncated on right is introduced. Its characteristics, namely, generating functions; and the measures of skewness and kurtosis have been obtained. The unknown parameter has been estimated using the method of maximum likelihood and the method of moments. The confidence interval of the estimate has been obtained through Fisher’s information matrix.
 The model is applied on cross sectional data obtained through Brief Psychiatric Rating Scale (BPRS) administered on a group of school going adolescent students; and the above-mentioned characteristics have been evaluated. An expert, on the basis of the BPRS score values, suggested an intervention program. The BPRS scores of the students who could be administered the intervention program lied in a range (which was above the lowest and below the highest possible values) suggested by the expert. Whereas the complete data suggested the average number of problem areas is four (which was not in consonance with the observations given by the expert), the double truncated model suggested the number of such areas as five which was consistent with the observations made by the expert. This establishes the usefulness of double truncated models in such scenarios.

Zero watermarking algorithm for BIM data based on distance partitioning and local feature

ABSTRACT Zero watermarking constructs the watermark information according to the characteristics of the original data, without changing the data structure and data accuracy. Maintaining high data accuracy is the premise of building information modelling (BIM) usability, so zero watermarking is a hotspot in the research of BIM data security protection. BIM model is a type of 3D model, however, most of the existing zero watermarking algorithms for 3D models are difficult to be better applied to BIM data due to data structure differences. To solve this problem, a zero-watermarking algorithm for BIM data based on distance partitioning and skewness measure is proposed. Firstly, after spatial partitioning based on element paradigm value, the mapping relationship between different partitions and watermarking bits is established. Then, the skewness of elements is calculated, and the skewness measure sign is used as the feature to obtain the binary sequence. Finally, the dissimilarity operation is performed on the binary sequence and the original watermarking sequence which was disordered to construct the zero watermark of the BIM data. The experimental results show that the zero watermarks constructed from different BIM data are unique and robust to translation, rotation, element deletion, element addition, and format conversion attacks. In addition, the superiority of this paper’s algorithm over the comparison algorithm in terms of robustness is compared. Therefore, the proposed algorithm can effectively provide technical support for BIM data copyright protection.

On the theory of order statistics of the flexible Lomax distribution

This paper studies the flexible Lomax distribution’s order statistics with graphical and numerical findings. Along with the quantitative measurements, some plots are furnished, including those for the skewness and kurtosis measures. We will dwell on the numerous results that relate to statistics of moments of order. We consider the single and product moment of order statistics from the new distribution. Further, we establish some recurrence relation for single moments of order statistics. We have sought to apply the derived relations to empirically evaluate the moments of smallest (largest) order statistics to establish well-known moments and related measures. For order statistics of a flexible Lomax distribution, exact analytical expressions of entropy, residual entropy, and past latent entropy are determined.

ANALISIS UMUR REPRODUKSI PALING AWAL DAN PALING AKHIR SERTA PUNCAK FERTILITAS PADA WANITA DI SETIAP KABUPATEN DAN KOTA DI PROVINSI BANTEN

The birth rate (fertility) is one of the factors that influences the increase in population. Banten Province has 8 districts and cities with different fertility rates. One of the fertility indicators presented in the Long Form SP2020 data is Birth Rate data by Age Group / Age Specific Fertility Rate (ASFR). The aim of this research is to determine the earliest, latest reproductive age and the age of women who have the highest fertility rates in each district and city in Banten Province. The skewness (measure of slope) and kurtosis (measure of sharpness) values of the continuous curve formed will also be studied. ASFR data presented by the Central Statistics Agency (BPS) is discrete data. Fertility rates will be approached using the MBF (Modified Beta Function) continuous fertility model. In this research, information was obtained that the earliest reproductive age in Banten Province was 15.64 years. This happened to women in Lebak Regency. Meanwhile, the latest reproductive age in Banten Province is 49.85 years. This happened to women in Pandeglang Regency. It can also be seen that the highest peak fertility rate for the population of Banten Province occurred in women aged 27.54 years in the Cilegon City area, with a peak fertility value of 0.13055. Apart from being based on calculations, this is in accordance with the curve visualization carried out using Mathematica software. The highest skewness value occurs in the continuous fertility curve for the Lebak Regency area. This means that Lebak Regency has the most left-leaning curve. All continuous fertility curves in districts and cities in Banten Province have a platykurtic distribution (flat curve) because the kurtosis value is smaller than 0.263

Property crime and lottery-related anomalies

In this paper, we explore the association between property crime rate and lottery demand anomalies. Motivated by criminology literature that suggests a positive relation between crime and risk-taking, we conjecture that gambling propensity in the stock market is stronger (weaker) in regions with higher (lower) property crime rate. Consistent with our conjecture, we show that underperformance of lottery stocks, proxied by MAX, is more pronounced in the US regions with higher property crime rates compared to regions with lower property crime rates. Our results are robust to alternative proxies for lottery demand, such as alternative constructions of MAX and skewness measures, and various empirical tests. Our findings suggest variation in crime-induced gambling propensity affects financial market outcomes.

Estimation of population variance using the actual ranks and values: Properties and application

Background: Of all measures of variability, the variance is by far the most popular. This paper argues an alternative index of variability, shares many properties with the variance, but can be more informative about the properties of distributions that depart from normality. Procedures: An estimator for the population variance is proposed. The proposed estimator is based, in its calculations, on the actual variable values and their ranks. A simulation study is employed to compare the performance of the proposed estimator with that of eight other estimators appearing in the literature using the mean square error criterion. The influence of sample size, normality, and non-normality is investigated. We suggest a new measure of skewness based on the new proposed estimator for the population variance. The mean value, median, and the new estimator for the population variance are the only three summary statistics that may be effectively used to derive the suggested coefficient of skewness. A limited Monte Carlo simulation is used to examine the potential of the suggested statistic to identify skewness. The covariance between a random variable and its rankings is how the new estimator is stated. This format is used to derive new correlation coefficients. Results and conclusion: The simulation study shows that the proposed estimator, under conditions of normality, performs better than most estimators considered, whereas it fails to give better results than some others. In cases of non-normality considered, the proposed estimator was superior to eight competitors. According to preliminary results, the new coefficient of skewness performs well overall in a limited simulation. The new correlation coefficient outperforms Pearson’s correlation for the non-normal model, as demonstrated by simulation analysis. Furthermore, it has been demonstrated that the new estimator is a useful tool for extracting a straightforward method to obtain novel skewness and correlation coefficients.