Group averaging and the Gini deviation

It is known that partitioning a society into groups with subsequent averaging in each group decreases the Gini coefficient. The resulting Lorenz function is piecewise linear. This study deals with a natural question: by how much the Gini coefficient could decrease when passing to a piecewise linear Lorenz function? Obtained results are quite illustrative (since they are expressed in terms of the geometric parameters of the polygon Lorenz curve, such as the lengths of its segments and the angles between successive segments) upper bound estimates for the maximum possible change in the Gini coefficient with a restriction on the group shares, or on the difference between the averaged values of the attribute for consecutive groups. It is shown that there exist Lorenz curves with the Gini coefficient arbitrarily close to one, and at the same time with the Gini coefficient of the averaged society arbitrarily close to zero.

Opportunity and inequality in the emerging esports labor market

Esports is often described as a growing industry ripe with financial opportunities for young professional, competitive gamers. However, these claims rarely consider how income is distributed amongst players. This study uses prize earnings data from 2005 to 2019 to examine labor market inequality and related social inequalities and social stratifications. Lorenz curves and Gini coefficients show that inequality has increased in the labor market overall and the labor markets for the five top games based on total prizes awarded ( Dota 2, Counter-Strike: Global Offensive, Fortnite, League of Legends, StarCraft II). Competitors can expect to earn more today than in 2005, but median incomes have shown sporadic and inconsistent growth compared with top incomes. Moreover, most competitors earn less than the US poverty threshold. Comparing the earnings of the top female players to the whole labor market shows that gender inequalities exist in median incomes and the likelihood of earning more than the poverty threshold. The esports labor market is an engine of inequality that provides opportunities for a few (primarily male) competitors while building a growing class of lowly paid players who support the interests of game designers and event organizers.

COVID-19 Cases Among Facility-Staff by Neighbourhood of Residence and Social and Structural Determinants: An Observational Study (Preprint)

BACKGROUND Disproportionate risks of COVID-19 in congregate settings including long-term care homes, retirement homes, and shelters both affect and are affected by SARS-CoV-2 infections among facility-staff. In cities across Canada, there has been a consistent trend of geographic clustering of COVID-19 cases. However, there remain limited data on how COVID-19 among facility-staff reflect urban neighbourhood disparities, particularly stratified by the social and structural determinants of community-level transmission. OBJECTIVE To compare the concentration of cumulative cases by geography and social/structural determinants across three mutually exclusive subgroups in the Greater Toronto Area (population 7.1 million): community, facility-staff, and healthcare workers (HCW) in other settings. METHODS We conducted a retrospective, observational study using surveillance data on laboratory-confirmed COVID-19 cases (January 23 to December 13, 2020; prior to vaccination roll-out). We derived neighbourhood-level social/structural determinants from census data, and generated Lorenz curves and Gini coefficients to visualize and quantify inequalities in cases. RESULTS The hardest-hit neighbourhoods (comprising 20% of the population) accounted for 53.4% of community cases, 48.6% of facility-staff cases, and 42.3% of other HCW cases. Compared with other HCW, cases in facility-staff more closely reflected the distribution of community cases. Cases in facility-staff reflected greater social and structural inequalities (larger Gini coefficients) than other HCW across all determinants. Facility-staff cases were also more likely than community cases to be concentrated in lower income neighbourhoods (Gini 0.24[0.15-0.38] vs 0.14[0.08-0.21] with lower household density (Gini 0.23[0.17-0.29] vs 0.17[0.12-0.22]) and with a greater proportion working in other essential services (Gini 0.29 [0.21-0.40], 0.22[0.17-0.28]). CONCLUSIONS COVID-19 cases among facility-staff largely reflects neighbourhood-level heterogeneity and disparities; even more so than cases in other HCW. Findings signal the importance of interventions prioritized and tailored to home geographies of facility-staff in addition to workplace measures, including prioritization and reach of vaccination at home (neighbourhood-level) and at work.

On the T-X Class of Topp Leone-G Family of Distributions: Statistical Properties and Applications

This article investigates the T-X class of Topp Leone- G family of distributions. Some members of the new family are discussed. The exponential-Topp Leone-exponential distribution (ETLED) which is one of the members of the family is derived and some of its properties which include central and non-central moments, quantiles, incomplete moments, conditional moments, mean deviation, Bonferroni and Lorenz curves, survival and hazard functions, moment generating function, characteristic function and R`enyi entropy are established. The probability density function (pdf) of order statistics of the model is obtained and the parameter estimation is addressed with the maximum likelihood method (MLE). Three real data sets are used to demonstrate its application and the results are compared with two other models in the literature.

On Beta Exponentiated Moment Exponential Distribution with Mathematical Characteristics and Application to Engineering Sectors

A new BEME distribution known as beta Exponentiated moment exponential (BEME) distribution is proposed. We provide here some shape properties, moments in the form of special functions, mean deviations of BEME distribution. We derive mathematical properties of the BEME distribution including the reliability measures, the Bonferroni and the Lorenz curves, rth order statistics, measures of uncertainty: the Shannon entropy measure and the s-entropy measure. The parameters of the BEME distribution are estimated by the method of maximum likelihood estimation and estimated non-linear equations for these estimates are presented. The application of BEME distribution is explored in three different fields of engineering.

Truncated Cauchy Power Odd Fréchet-G Family of Distributions: Theory and Applications

The truncated Cauchy power odd Fréchet-G family of distributions is presented in this article. This family’s unique models are launched. Statistical properties of the new family are proposed, such as density function expansion, moments, incomplete moments, mean deviation, Bonferroni and Lorenz curves, and entropy. We investigate the maximum likelihood method for predicting model parameters of the new family. Two real-world datasets are used to show the importance and flexibility of the new family by using the truncated Cauchy power odd Fréchet exponential model as example of the family and compare it with some known models, and this model proves the importance and the flexibility for the new family.

Marshall-Olkin Lindley-Log-logistic distribution: Model, properties and applications

The authors introduce a new generalized distribution called the Marshall-Olkin Lindley-Log-logistic (MOLLLoG) distribution and discuss its distributional properties. The properties include hazard function, quantile function, moments, conditional moments, mean and median deviations, Bonferroni and Lorenz curves, distribution of the order statistics and Rényi entropy. A Monte Carlo simulation study was used to examine the bias, relative bias and mean square error of the maximum likelihood estimators. The betterness of the new distribution compared to other distributions is illustrated by means of two real life datasets.

The Kumaraswamy Pareto IV Distribution

We introduce a new model named the Kumaraswamy Pareto IV distribution which extends the Pareto and Pareto IV distributions. The density function is very flexible and can be left-skewed, right-skewed and symmetrical shapes. It hasincreasing, decreasing, upside-down bathtub, bathtub, J and reversed-J shaped hazard rate shapes. Various structural properties are derived including explicit expressions for the quantile function, ordinary and incomplete moments,Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time, probability weighted moments and generating function. We provide the density function of the order statistics and their moments. The Renyi and q entropies are also obtained. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The usefulness of the new model is illustrated by means of three real-life data sets. In fact, our proposed model provides a better fit to these data than the gamma-Pareto IV, gamma-Pareto, beta-Pareto,exponentiated Pareto and Pareto IV models.

Public Transport Network Vulnerability and Delay Distribution among Travelers

Methodologies and approaches for assessing the vulnerability of a public transport network are generally based on quantifying the average delay generated for passengers by some type of disruption. In this work, a novel methodology is proposed, which combines the traditional approach, based on the quantitative evaluation of averaged disruption effects, with the analysis of the asymmetry of effects among users, by means of Lorenz curves and Gini index. This allows evaluating whether the negative consequences of disruptions are equally spread among passengers or if differences exist. The results obtained show the potential of the proposed method to provide better knowledge about the effects of a disruption on a public transport network. Particularly, it emerged that disrupted scenarios that appear similar in terms of average impacts are actually very different in terms of the asymmetry of effects among users.