The Weibull distribution is extensively useful in the field of finance, insurance and natural disasters. Recently, It has been considered as one of the most frequently used statistical distributions in modelling and analyzing stock pricing movement and uncertain prediction in financial and investment data sets, such as insurance claims distribution. It is well known that the Bayes estimators of the two-parameter Weibull distribution do not have a compact form and the closed-form expression of the Bayes estimators cannot be obtained. In this paper and the Bayesian setting, it is assumed that the scale parameter of the Weibull model has a gamma prior under the assumption that its shape parameter is known. A simulation study is performed using random claims amount to compare the performance of the Bayesian approach with traditional maximum likelihood estimators in terms of Root Mean Square Errors (RMSE) and Mean Absolute Error (MAE) for different sample sizes, with specific values of the scale parameter and shape parameters. The results have been compared with the estimated result via the maximum likelihood method. The result revealed that the Bayesian approach behaves similarly to the maximum likelihood method when the sample size is small. Nevertheless, in all cases for both methods, the RMSE and MAE decrease as the sample size increases. Finally, applications of the proposed model to the insurance claim data set have been presented.

The implementation of environmental protection strategy necessarily requires mapping the amount of capital stock of environmental infrastructure. Through the Weibull distribution function and hyperbolic age-decreasing efficiency model, the provincial environmental infrastructure capital stock in China from 1980 to 2018 is measured cautiously, and its spatial dynamics with the generated pollutants is analyzed using the center of gravity method. It is found that: the spatial distribution of environmental infrastructure capital stock is uneven, and the unevenness in the east-west direction is greater than that in the north-south direction, but the unevenness in the east-west direction is narrowing while the north-south direction is widening; the spatial and temporal distribution of environmental infrastructure capital and environmental pollution vary greatly, and the spatial management of environmental pollution is less accurate.

Poland has experienced a very sharp rise in income and wealth inequality after the economic transition. We measure the relative persistence of income inequality and intra-generational income mobility in Poland during the period 2008-2015. Our research is based on the panel survey data, our subsample includes 501 households. To measure the persistence of income inequality we calculate Shorrocks’s R coefficient. We find that if inequality is measured by the Gini index the relative persistence of income inequality in Poland is similar to Western Europe. In the case of the Theil index and the Mean Log Deviation (MLD), the relative persistence is higher than in a majority of Western Europe countries and similar to the United Kingdom or the United States. The income distribution in Poland is rather stable. Income mobility is lowest at the bottom and at the top of the income distribution. In the middle (3rd) quintile upward mobility is higher than downward mobility. The short-term income mobility in Poland has not changed during and after the Great Financial Crisis and is still medium in comparison with the rest of Europe.

Calculating the amount of regulatory capital to cover unexpected losses due to operational events in the upcoming year has caused problems because of difficulties in fitting probability distributions to data. It is consequently difficult to judge an appropriate level of capital that reflects the risk profile of a financial institution. We provide theoretical and empirical analyses to link the calculated capital to the sum of losses using appropriate statistical approximations. We conclude that, in order to reasonably reflect the associated risk, the capital should be approximately half the sum of losses, with a wide bound for the ratio of capital to sum.