This paper proposes a very simple way to estimate the Gini Coefficient, particularly when the data are divided into K open-ended income intervals without information about the interval mean incomes: The measure proposed is based upon the assumption that income is distributed according to the log-logistic Distribution. This assumption can be readily checked using a simple plotting procedure and the Gini can then be estimated by applying OLS to the plot. The model is shown to work very well for two very different sets of data from the UK and Iran. The log-logistic has the following important implication in the present context. Any income level (y) divides the population into two parts. The ratio of the population with income less than or equal to y to those with income more than y is a log-linear function of the y .The slope of the line can be interpreted as an equality index and the inverse of the slope is the well-known Gini Coefficient. This can be compared with the Pareto Law of income Distribution, which states that the proportion of people' with income greater than y will be a linear function of y on double log scale. However, whereas the Pareto Law applies merely to the upper-tail segment of the income Distribution, the log-logistic constitutes a model, which pertains to the complete range of incomes.

Background: Each country’s health system is tasked with providing services to ensure the health of its population. Dental services are among these essential services. However, dental service utilization is unevenly distributed worldwide. This study’s findings will give health sector officials and policymakers valuable insights to enhance system performance.Methods: This descriptive-analytical study, conducted in 2021, aimed to determine the Distribution of dentists worldwide. The analysis utilized the Pareto curve, the dentist-to-population ratio (DPR), the Gini Coefficient (GC), and the Lorenz curve. The goal was to identify the countries with the highest number of dentists.Results: There are over 2,500,000 dentists globally, averaging 3.6 dentists per 10,000 people. However, the ratios vary significantly, with about 6.8 per 10,000 in countries with very high Human Development Index (HDI) groups and 0.19 per 10,000 in low HDI groups. The data indicates that more than 80% of dentists work in countries with very high and high HDI.Conclusion: This study suggests that job concentration is higher in areas with superior welfare and facilities, and dentistry is no exception. Therefore, creating better welfare in more disadvantaged areas, implementing mandatory government plans, and strategic government planning can help mitigate Distribution inequality.

Background & Aim: A single outlier can even have a large disturbing effect on a classical statistical method that is optimal under the classical assumptions. One of the powerful goodness-of-fit tests is the correlation Coefficient test, however this test suffers from the presence of outliers.Methods & Materials: This study provides a simple robust method for test of goodness of fit for the Gumbel Distribution [extreme value Distribution (EVD) type I family] through using the new diagnostic tool called the "Forward Search" (FS) method. The FS version of this test was introduce in the present study, which is not affected by the outliers.Results: A new robust method for testing the goodness-of-fit for Gumbel Distribution has been presented. The approach gives information about the Distribution of majority of the data and the percentage of contamination.Conclusion: A new robust method for testing the goodness-of-fit for the Gumbel Distribution has been presented. The simple and fast method have been used to find Distribution of proposed statistic. In addition, using the transformation study, an application to the two-parameter Weibull Distribution has been investigated. The performance and the ability of this procedure to capture the structure of data have been illustrated by some simulation studies.

This study investigates the Distribution Coefficient of strontium in a soil sample in the south of Tehran. In this research, the columnar method was used to determine the Distribution Coefficient of strontium. Also, the effect of three factors, pH, strontium concentration, and soil height in the column was studied using the RSM method's experimental design. For this purpose, five different levels were considered for each parameter, and the experiments were designed and performed by MiniTab software. According to the results obtained in the predicted model, pH, column height, interaction between pH and column height, the interaction between pH and strontium concentration, and interaction between strontium concentration and column height are important. The square of the Coefficients as well as the concentration of strontium, did not have much effect on the Distribution Coefficient. The most significant effect is due to the height of the column, which increases with increasing the height of the column. The rate of conformity of the predictive equation with the actual values is 96. 39%, which is an acceptable value.

Calculation of Distribution Coefficients is one of the essential provisions in the safety assessment of radioactive waste repository and safe management of radioactive waste. Due to the importance and characteristics of thorium radionuclide in radioactive waste inventory, the Distribution Coefficient of thorium in the alluvium soil of Anarak Radioactive Waste Repository was determined by the Batch method two parameters of thorium concentration and soil granulation were studied. Also, the Flow-Through method studied the adsorption behavior of thorium has investigated the effect of thorium concentration and soil height. The average value of thorium Distribution Coefficient in Anarak soil was calculated 110960 L/kg using the Batch method. The study of adsorption behavior by the Flow-Through method demonstrated high uptake of thorium in the soil due to the strong bond created between the ion and the adsorbent. The results showed that the Distribution Coefficient increases with the decrease of soil particle size. Regarding the effect of concentration on the thorium Distribution Coefficient, first, an increasing trend and a decreasing trend were observed in the test range. The results obtained in this study were compared with the results of other studies on thorium radionuclide, which showed a good agreement with other studies.

The subject of this article is to assess Personal Income Distribution in I.R. Iran both in rural and urban areas using Gini Coefficient and Atkinson index in the period of 2001-2013. These two indices satisfy Dalton principles (principles about requirements of a good income Distribution index) and comparing to other income Distribution indices are more precise. Although Gini Coefficient is the most common measure of income inequality, since it is highly sensitive to inequalities in the middle of the income spectrum, it may not be able to distinguish between two different income Distributions. But the Atkinson index considering social welfare function into the measurement of income inequality allows for varying sensitivity to inequalities in different levels of the income Distribution and it can be a complement to Gini Coefficient. Results based on Gini and Atkinson show decreasing income inequality during the investigated period both in rural and urban areas. Income inequality in urban areas is less than rural areas and considering different income levels, the income inequality rises in both areas as the level of income increases. Since the year 2010, income inequality has been decreasing in both areas and there was a more sensible decrease in 2011 which could be due to performing the subsidy reform program and a payment of 455000 Rials per person to Iranian families since December 2010 (as Dalton’s third principle of equal payments suggests)

Income Distribution is a considerable and sustainable problem in many countries. Hence, Governments around the world tend to target interventions that aim to reduce or alleviate inequality. Income Distribution has been a long running interest of both academia and politicians. Using three measures of inequality, Gini Coefficient; Theil and Atkinson Indices, the condition of income Distribution within groups of household with different socio-economic characteristics provided. The data used in this paper have been collected in an Income-Expenditure Survey by Statistical centre of Iran.The findings of this paper indicate that the Income Distribution depends largely on household characteristics. Summarizing the main results of this paper, we see that Distribution of income within groups of households whose heads are under 25, employed in agriculture and/or Construction sector of economy is severe. In addition, inequality in less deprived regions is more severe than deprived regions.

One of the obvious reasons for most disorders in network service provisioning is network path congestion. Congestion avoidance in today's networks is too costly and sometimes impossible. With the introduction of SDN, centralizing the equipment's control plane has become possible. This paper presents an enhanced method named ESV-DBRA to avoid congestion in multi-tenant SDN networks. At first, ESV-DBRA monitors the traffic load and delay of all network paths for each tenant individually. Then, by merging the parameters obtained from the monitoring, the Service Level Agreements (SLA), and a novel proposed cost function, it calculates the cost of the network paths per tenant. As a result, traffic for each tenant is routed through the path/paths at the lowest possible cost from the tenant's perspective. Next, the bandwidth quotas will be calculated and assigned to the tenants over their optimal routes. Afterward, whenever congestion is likely to occur in a path, ESV-DBRA automatically changes the route or bandwidth of the tenants' traffic related to this path to avoid congestion. Related algorithms are also proposed.Eventually, simulations show that the proposed method effectively increases bandwidth utilization by 10.76%.

Statistical Distributions have important role in data analysis. Generalized Distributions are very flexible Distributions for several kinds of random variables. The most important Distribution is the generalized beta Distribution which is used for positive random variables. The generalized beta of the first kind "GB1" and second kind "GB2" are special cases of the generalized beta Distribution. The "GB2" includes the "B2" and the "Generalized Gamma" as limiting cases. The "GB1" includes the "B2", the two Burr" Distributions, Generalized Gamma, Fisk, Weibull and Log-normal Distribution as special cases. Figure 4 shows the relation of the above Distributions. By using the data of family incomes interval in Khuzestan, the best Distribution is estimated and the Gini Coefficient is computed and the interpretation of the results are discussed