Novel composite model: application in epidemic and actuarial science


  • Moulouk Halima Benchettah
  • Halim Zeghdoudi
  • Raman Vinoth



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


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.


CEBRIAN, A.; DENUIT, M.; LAMBERT, P. Generalized Pareto fit to the society of Actuaries' large claims database. North American Actuarial Journal, v. 7, p. 18-36, 2003.

ELBATAL, I.; ARYAL, G. A new generalization of the exponential Pareto distribution. Journal of Information and Optimization Sciences, v. 38, n. 5, p. 675-697, 2017. DOI:10.1080/02522667.2016.1220079

Cooray, K.; Ananda. M. A. Modeling actuarial data with a composite Lognormal-Pareto model. Scand. Actuar. J., v. 5, p. 321–334, 2005.

KLUGMAN, S. A.; PANJER, H. H.; WILLMOT, G. E. Loss Models: From Data to Decisions. New York: Wiley,1998.

MCNEIL, A. J. Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory. Astin Bulletin, v. 27, n. 1, p. 1-21, 1997.

Rashad, M. E.-S., Mahmoud, M. A. W.; & Abdallah, S. H. M. Statistical inferences for new Weibull-Pareto distribution under an adaptive type-ii progressive censored data. Journal of Statistics and Management Systems, v. 21, n. 6, p. 1021-1057, 2018. DOI:10.1080/09720510.2018.1467628

SCOLLNIK, D. P. M. On composite Lognormal-Pareto models. Scan-dinavian Actuarial Journal, p. 20–33, 2007.

TEODORESCU, S.; VERNIC, R. Some composite Exponential-Pareto models for actuarial prediction. Rom. J. Econ. Forecast., v. 12, p. 82–100, 2009.

TEODORESCU, S.; VERNIC, R. A composite Exponential-Pareto distribution. The Annals of the “Ovidius” University of Constanta, Mathematics Series, v. XIV, n. 1, p. 99-108, 2006.

TEODORESCU, S.; VERNIC, R. On composite Pareto models. Math.Reports, v. 15, n. 65, 1, p. 11–29, 2013.

PREDA, V.; CIUMARA, R. On composite models: Weibull-Pareto and Lognormal-Pareto. A comparative study. Rom. J. Econ. Forecast., v. 3, p. 32–46, 2006.




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.