Probability-based distributions might be able to explain risk exposure well. Usually, one number, or at the very least, a limited number of numbers called the key risk indicators (KRIs), are used to describe the level of risk exposure. These risk exposure values, which are undeniably the outcome of a specific model, are frequently referred to as essential critical risk indicators. Five key risk indicators, including value-at-risk, tail variance, tail-value-at-risk, and tail mean-variance, were also used for describing the risk exposure under the reinsurance revenues data. These measurements were created for the proposed model; hence, this paper presents a novel distribution for this purpose. Relevant statistical properties are derived, including the generating function, ordinary moments, and incomplete moments. Special attention is devoted to the applicability of the new model under extreme data sets. Three applications to real data show the usefulness and adaptability of the proposed model. The new model proved its superiority against many well-known related models. Five key risk indicators are employed for analyzing the risk level under the reinsurance revenues dataset. An application is provided along with its relevant numerical analysis and panels. Some useful results are identified and highlighted.

This study seeks to determine how economic policy uncertainty (EPU) influences investment decisions and the market value of the Pakistan Stock Exchange. This study examines investment and operational data from 249 energy and petroleum companies between 2015 and 2020 and macroeconomic variables such as EPU. This study investigates the moderating effects of EPU on investments in fixed and intangible assets and its effect on Tobin’s Q and the market price per share. The outcomes demonstrate that EPU reduces the costs of both tangible and intangible assets for businesses. In addition, companies with a higher Tobin’s Q and market price per share are more impacted by uncertain corporate investment policies. However, financial leverage is negatively correlated with share price and positively correlated with earnings per share and earnings per unit. Tobin’s Q positively correlates with financial leverage, indicating that firms that raise capital through debt are more likely to create value for investors. The research indicates that market-dependent enterprises are more susceptible to the unpredictability of monetary policy. According to this study, consistent application and open communication of economic policies are likely to increase the efficacy of company investments, resulting in more effective resource allocation and business decision-making.

The idea of symmetry, which is used to describe the shape of a probability distribution, is a key concept in the theory of probability. The use of symmetric and asymmetric distributions is common in statistical inference, decision-making, and probability calculations. This article introduces a novel asymmetric model for assessing risks under a skewed claims dataset. The new distribution is also employed for both censored and uncensored validation testing. Four estimation methods, maximum likelihood, ordinary least squares, L-Moment, and Anderson Darling, were used for the risk assessment and analysis. To explain the exposure to risk within actuarial claims data, we introduced five crucial indicators, namely value-at-risk, tail-value-at-risk, tail variance, tail mean-variance, and mean excess losses. A numerical and graphical analysis is presented to assess the actuarial risk. Furthermore, the article discusses a newly developed Rao Robson Nikulin statistic for censored and uncensored validation testing. The validation testing also involved the insurance claims dataset.