EFEP distribution

We defined Twisted Wang Transform Distribution (TWTD) family, and found for a hurricane reinsurance-portfolio-loss the EFEP distribution in that family is the best fit. The TWTD use elementary functions such as power, exponential, and fraction to define the distribution, on CDF, not on PDF that people are usually dealing with. This research is shared on website https://www.preprints.org/manuscript/202207.0032/v1.

Recently for a different peril, a by county portfolio loss, we find the EFEP is still the best-fit distribution.?

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Figure 1. SmoothKernel (in black), EFEP (in blue), ExponentiatedGeneralizedGamma (in red), moment matched DoublePareto (in yellow) PDF plots.

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Figure 2. SmoothKernel (in black), EFEP (in blue), ExponentiatedGeneralizedGamma (in red), maximum likelihood fitted ShiftedDoublePareto (in yellow), DoublePareto (in green) PDF plots.

One occurrence may be by chance, but another unrelated incidence may indicate that EFEP is indeed good for hard-to-fit cases. So more study are done for EFEP, from the same idea of using elementary function as transformations, we extended the definition of skewness, kurtosis, and shape factors to normalized skewness, normalized kurtosis, and normalized shape factors, with values inside the unit interval. A simple power function relationship among these stats are discovered. The good and bad fit make us conjecture that the first four central moments are not enough to restrict the distribution PDF shape, but with the addition of the first three absolute central moments it may be enough. These researches will be in a forthcoming paper “Shape factor asymptotic analysis III” soon.