Novel composite model: application in epidemic and actuarial science

Authors

  • Moulouk Halima Benchettah
  • Halim Zeghdoudi
  • Raman Vinoth

DOI:

https://doi.org/10.54021/seesv5n1-095

Keywords:

composite distribution, Pareto distribution, Nakagami distribution, maximum likelihood estimation, Marburg virus, fire insurance losses

Abstract

Actuarial sciences frequently use Nakagami and Pareto distributions to model their payment data. The Nakagami distribution is frequently employed for modeling the lifespans of things that are affected by their age, and it possesses a multitude of practical applications. Alternatively, academics sometimes utilize the Pareto distribution to model payments data, especially for instances of substantial loss data or reinsurance payments. The present study presents and investigates a new composite model known as the composite Nakagami-Pareto distribution (CNPD), which integrates components from both the Nakagami and Pareto distributions. When examining composite distributions, the first distribution is usually characterized by a thin tail, whereas the next distribution has a thick tail. In the Nakagami-Pareto model, the Nakagami density is chosen as  due to its characteristic of being a light-tailed distribution. Similarly, the Pareto distribution is selected as  because it exhibits a heavy-tailed distribution. An investigation has been conducted to assess the practical usefulness of the composite Nakagami-Pareto model when applied to real-world data sets. This analysis has emphasized the significant components of the model. Statistical qualities such as cumulative distribution function, quantile function, mode, first moment, ad-hoc procedure and maximum likelihood estimation have been established. Furthermore, a method for estimating has been described utilizing a data sample derived from the Composite Nakagami-Pareto model. The composite exponential-Pareto and the composite lognormal-Pareto distributions' resultant densities have similar shapes, but their tails are more noticeable. Therefore, we anticipate that our model will be more suitable than the composite exponential-Pareto distribution, composite lognormal-Pareto distribution, and other traditional one (or two)-parameter distributions. The significance and practicality of this novel approach were demonstrated by analyzing simulated cases, data sets are available for the recovery periods (measured in weeks) of 75 persons from Angola who were infected with the Marburg virus, as well as for 2156 fire insurance losses in Denmark.

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Published

2024-05-16

How to Cite

Benchettah, M. H., Zeghdoudi, H., & Vinoth, R. (2024). Novel composite model: application in epidemic and actuarial science. STUDIES IN ENGINEERING AND EXACT SCIENCES, 5(1), 1904–1917. https://doi.org/10.54021/seesv5n1-095