Abstract
Actuaries are often in search of nding an adequate loss model in the scenario of actuarial and financial risk management problems. In this work, we propose a new approach to obtain a new class of loss distributions. A special sub-model of the proposed family, called the Weibull-loss model isconsidered in detail. Some mathematical properties are derived and maximum likelihood estimates of the model parameters are obtained. Certain characterizations of the proposed family are also provided. A simulation study is done to evaluate the performance of the maximum likelihood estimators. Finally, an application of the proposed model to the vehicle insurance loss data set is presented.
Highlights
Speaking broadly, modeling insurance loss data with a heavy tail is a prominent research topic
In this sub-section, we evaluate the performance of the maximum likelihood estimators presented in sub-section 4.1 for W-Loss distribution with respect to the sample size n
The mean square errors (MSEs), biases and absolute biases of the model parameter estimates are calculated by means of R software
Summary
Speaking broadly, modeling insurance loss data with a heavy tail is a prominent research topic. Numerous heavy-tailed models have been proposed in the literature such as Pareto, lognormal, Lomax, Burr, Weibull, and gamma distributions, for a brief discussion, we refer the interested readers to Hogg and Klugman (2009) Amongst these distributions, the Pareto distribution does not provide a better fit for many applications due to the monotonically decreasing shape of the density function, in particular when the shape of the data is hump-shaped, see, Cooray and Ananda (2005). The new distributions introduced through these methods involve two or more extra parameters and the form of the density function becomes more complicated causing difficulties in estimating the model parameters To overcome these issues, we propose a new method of constructing new distributions.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Pakistan Journal of Statistics and Operation Research
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
