Abstract
Statistical distributions play a prominent role for modeling data in applied fields, particularly in actuarial, financial sciences, and risk management fields. Among the statistical distributions, the heavy-tailed distributions have proven the best choice to use for modeling heavy-tailed financial data. The actuaries are often in search of such types of distributions to provide the best description of the actuarial and financial data. This study presents a new power transformation to introduce a new family of heavy-tailed distributions useful for modeling heavy-tailed financial data. A submodel, namely, heavy-tailed beta-power transformed Weibull model is considered to demonstrate the adequacy of the proposed method. Some actuarial measures such as value at risk, tail value at risk, tail variance, and tail variance premium are calculated. A brief simulation study based on these measures is provided. Finally, an application to the insurance loss dataset is analyzed, which revealed that the proposed distribution is a superior model among the competitors and could potentially be very adequate in describing and modeling actuarial and financial data.
Highlights
Heavy-tailed distributions have been studied for decades by actuaries to investigate various aspects of financial portfolio theory and risk management problems
As an example, (i) the Pareto model, which is one of the prominent models used for modeling financial data, sometimes provides poor fitting to many financial applications, (ii) on the other hand, the Weibull model can only cover the behavior of small losses adequately but is not a reasonable candidate model to deal with the behavior of large losses, and (iii) the distribution functions of both the lognormal and the beta distributions have no closed form expressions causing difficulties in the derivation of many mathematical properties and make them less popular to use for analyzing financial datasets (Bhati and Ravi [18])
We study a new model called the heavy-tailed betapower transformed Weibull (HTBPT–Weibull) distribution as a special case of the heavy-tailed beta-power transformed (HTBPT) distributions. e proposed model is very flexible and could be chosen as a good candidate model for modeling heavy-tailed data
Summary
Heavy-tailed distributions have been studied for decades by actuaries to investigate various aspects of financial portfolio theory and risk management problems. Refer to the studies by Shushi [14], Punzo et al [15], Punzo et al [16], and Punzo [17] Despite these classical distributions having many merits, there are still some deficiencies in these models as they are not flexible enough to provide the best fit to the heavy-tailed datasets. We study a new model called the heavy-tailed betapower transformed Weibull (HTBPT–Weibull) distribution as a special case of the HTBPT distributions.
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