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.

Time series are essential for anticipating various claims payment applications. For insurance firms to prevent significant losses brought on by potential future claims, the future values of predicted claims are crucial. Additionally, the ideal parameter is chosen artificially. By using a genuine application, the proposed model’s utility is demonstrated. Additionally, the ideal parameter is chosen artificially. By using a genuine application, the proposed model's utility is demonstrated. Also, the single exponential smoothing model is used for prediction under the Holt-Winters’ additive algorithm.

Support Vector Regression (SVR) formulates is an optimization problem to learn a regression function that maps from input predictor variables to output observed response values. The SVR is useful because it balances model complexity and prediction error, and it has good performance for handling high-dimensional data. In this paper, we use the SVR model to improve the principal component analysis and the factor analysis methods. Simulation experiments are performed to assessment the new method. Some useful applications to real data sets are presented for comparing the competitive SVR models. It is noted that with increasing sample size, the -SVR type under the principal component analysis is the best model. However, under the small sample sizes the SVR type under the factor analysis provided adequate results.

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