Moustafa Salem, Walid Emam, Yusra Tashkandy, Mohamed Ibrahim, M. Masoom Ali, Hafida Goual, Haitham M. Yousof

A New Lomax Extension: Properties, Risk Analysis, Censored and Complete Goodness-of-Fit Validation Testing under Left-Skewed Insurance, Reliability and Medical Data

  • Physics and Astronomy (miscellaneous)
  • General Mathematics
  • Chemistry (miscellaneous)
  • Computer Science (miscellaneous)
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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.

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