© Jitendra Kumar, Anuj Nain. Article available under the CC BY-SA 4.0 licence
ARTICLE
ABSTRACT
The search for relevant models that can describe the loss data has been one of the main interests of researchers for decades. There is limited research on modeling such data using K-component mixture models. An example of that can be Miljkovic and Grün’s study (2016) of six distributions where they proposed finite mixtures to model the data. In this paper we study two more distributions, namely log-logistic and inverse Weibull distribution in addition of all those proposed by Miljkovic and Grün (2016). We employed the EM algorithm for parameter estimation and then selected the best model using three model selection criteria, namely NLL, AIC and BIC. We also computed the risk measures such as VaR and TVaR and compared them with their empirical counterparts to assess the goodness-of-fit of our proposed models at the extreme quantiles. We found that K-component mixture distribution of loglogistic and inverse Weibull works better than competent models. To get a more generalized view on the theory of mixture distribution, a simulation was carried out, which gave satisfactory results.
KEYWORDS
K-component finite mixture models, EM algorithm, Danish fire insurance losses data set, log-logistic distribution, inverse Weibull distribution.
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