Document Type
Article
Publication Date
1-2021
Publisher
Korean Statistical Society
Source Publication
Communications for Statistical Applications and Methods
Source ISSN
2287-7843
Abstract
Heavy tailed distributions are useful for modeling actuarial and financial risk management problems. Actuaries often search for finding distributions that provide the best fit to heavy tailed data sets. In the present work, we introduce a new class of heavy tailed distributions of a special sub-model of the proposed family, called a new extended alpha power transformed Weibull distribution, useful for modeling heavy tailed data sets. Mathematical properties along with certain characterizations of the proposed distribution are presented. Maximum likelihood estimates of the model parameters are obtained. A simulation study is provided to evaluate the performance of the maximum likelihood estimators. Actuarial measures such as Value at Risk and Tail Value at Risk are also calculated. Further, a simulation study based on the actuarial measures is done. Finally, an application of the proposed model to a heavy tailed data set is presented. The proposed distribution is compared with some well-known (i) two-parameter models, (ii) three-parameter models and (iii) four-parameter models.
Recommended Citation
Ahmad, Zubair; Mahmoudi, Eisa; and Hamedani, Gholamhossein, "A New Extended Alpha Power Transformed Family of Distributions: Properties, Characterizations and an Application to a Data Set in the Insurance Sciences" (2021). Mathematical and Statistical Science Faculty Research and Publications. 125.
https://epublications.marquette.edu/math_fac/125
Comments
Published version. Communications for Statistical Applications and Methods, Vol. 28 (January 2021): 1-19. DOI. © 2021 Korean Statistical Society. Used with permission.