Abstract
In this study, we propose a new heavy-tailed distribution, namely, the type I heavy-tailed odd power generalized Weibull-G family of distributions. Several statistical properties including hazard rate function, quantile function, moments, distribution of the order statistics and Renyi entropy are presented. Actuarial measures such as value at risk, tail value at risk, tail variance and tail variance premium are also derived. To obtain the estimates of the parameters of the new family of distributions, we adopt the maximum likelihood estimation method and assess the consistency property via a Monte Carlo simulation. Finally, we illustrate the usefulness of the new family of distributions by analyzing four real life data sets from different fields such as insurance, engineering, bio-medical and environmental sciences.
Publisher
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
Reference31 articles.
1. Afify, A.Z., Gemeay, A.M., Ibrahim, N.A., The heavy-tailed exponential distribution: risk measures, estimation, and application to actuarial data, Mathematics, 8(8) (2020), 1276. https://doi.org/10.3390/math8081276
2. Ahn, S., Kim, J.H., Ramaswami, V., A new class of models for heavy-tailed distributions in finance and insurance risk, Insurance: Mathematics and Economics, 51(1) (2012), 43-52. https://doi.org/10.1016/j.insmatheco.2012.02.002
3. Akaike, H., A new look at the statistical model identification, IEEE Transactions on Automatic Control, 19(6) (1974), 716–723. DOI:10.1109/TAC.1974.1100705
4. Al-Mofleh, H., Elgarhy, M., Afify, A., Zannon, M., Type II exponentiated half logistic generated family of distributions with applications, Electronic Journal of Applied Statistical Analysis, 13(2) (2020), 536-561. DOI:10.1285/i20705948v13n2p536
5. AL-Kazrajy, A.A., Comparative study of estimation methods of reliability with complete data using simulation (With Application), MSc thesis(2001), Mosul University, Iraq.