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.

This paper analyses a model of private value auctions with symmetric risk-neutral bidders, where bidders' private values of an indivisible good are fuzzy. The auction is studied as a game with incomplete information. Fuzzy random variables, their quantile functions, and expressions for expectations through quantile functions are used. An explicit expression for the solution is found. Also, expected bidders' payments are studied.

Liquidity can be a real phenomenon for execution of the financial holding. Its risk falls in debate to impose a conditional cost on the counterparty. The time-varying liquidity is often linked to the expected fundamental value of an investment. In this work, the microblogging-based informed transaction is examined as a determinant of the liquidity-facilitating cost. Most importantly, this study investigates the economic blockade era and post-pandemic uncertainty. The sentiment indicators were found to be determinants of liquidity. These findings were consistent in the post-pandemic period. However, the investor pessimistic sentiment was a priced risk factor in liquidity during the economic blockade period. Based on the Bayesian theorem, a relativeness was reported between sentiment indicators and the liquidity-facilitating cost. The same findings were depicted in environments of the pandemic era. Nevertheless, the posterior probability indicated an occurrence of the liquidity-associated cost in response to the pessimistic sentiments during the economic blockade period. This quantification may have potential implications in terms of exploring liquidity from the microblogging perceptive.

In the behavioral domain, this study discloses the pattern between microblogging-opinionated information and yields on the investment. This phenomenon is particularly related to the political instability in the Pakistan’s economy through the multivariate techniques. Pre-political crisis, the pessimistic sentiments were priced in yields on the investment. In environments of political instability, the intensity of decline in yields was more responsive against an incline in the negative opinions. Meanwhile, the intensity of increase in returns was less responsive against an incline in the positive opinions. The findings were further supported by the Bayesian approach. Before the political instability takes place in the Pakistan’s economy, the occurrence of yields was noted in response to the bearish market period. Post-political instability, there was a higher posterior probability for occurrence of returns against the bearish market period. Conversely, a higher posterior likelihood was noted for occurrence of investment’s yields in response to the bullish market period, but this relevance was not completely probable. From the impulse response analysis, the response of returns was reported against the standard deviation shocks in the microblogging sentiment indicators. The analysis may have potential implications in terms of disclosing the investors’ behavior from a political perspective.