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.

Spence’s signaling model (Spence, 1973) suggests that education can signal workers’ unobserved ability to employers thereby mitigating discrimination. There have been several studies concerning education’s impact on labor market discrimination against minority or disadvantaged groups. Our approach in this inquiry is unique in that we utilize the data of PhD recipients, a group of people with the highest education attainment, to test Spence’s theory. Another novelty of this paper is that in addition to examining possible discrimination against women and foreign-born, as has been done in previous studies, we further explore possible discrimination against the physically challenged individuals. Our baseline results show conflicting results that Ph.D. education can reduce discrimination against disability and foreign-born but not against gender. Further analysis by the Blinder-Oaxaca Decomposition shows that the wage gaps of gender and disability come more from the unobserved part than the explained part, while the foreign-born wage gap come more from the observable human capital differences. Since prejudice is an unobserved factor and we know that the disadvantaged groups are likely to suffer from prejudice (Oaxaca, 1973; Blinder, 1973; Montes-Rojas et al., 2017; Deshpande and Khanna, 2018), we conjecture that prejudice might be attributable to the unexplained part of the wage gaps. Furthermore, prejudice might be deeply rooted in one’s mind, thus difficult to remove even with the influence of education. Hence, our results reveal that it would be hard for Ph.D. education to eradicate the discrimination against gender and disability, but not against foreign-born.