Modeling loss data using mixtures of distributions

Miljkovic, Tatjana; Grün, Bettina

doi:10.1016/j.insmatheco.2016.06.019

Cited by 88 publications

(45 citation statements)

References 20 publications

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“…In this section, we propose several two component mixture models and provide their basic statistical properties. Two component mixture models have shown sufficient reliability in terms of goodnessof-fit to loss data, see Miljkovic and Grün (2016). In general, the mixture model has the following general probability density function…”

Section: Methodsmentioning

confidence: 99%

“…All the studies mentioned so far employ models that feature unimodality. More recently, Miljkovic and Grün (2016) initiated the use of non-Gaussian mixture models to describe this feature on the Danish loss data and showed their significance in risk estimation. The authors proposed the use of the Expected-Maximization algorithm using three initialization strategies for parameter estimation.…”

Section: Introductionmentioning

confidence: 99%

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Risk measure estimation under two component mixture models with trimmed data

Bakar

Nadarajah

2018

Journal of Applied Statistics

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Several two component mixture models from the transformed gamma and transformed beta families are developed to assess risk performance. Their common statistical properties are given and applications to real insurance loss data are shown. A new data trimming approach for parameter estimation is proposed using the maximum likelihood estimation method. Assessment with respect to Value-at-Risk and Conditional Tail Expectation risk measures are presented. Of all the models examined, the mixture of inverse transformed gamma-Burr distributions consistently provides good results in terms of goodness-of-fit and risk estimation in the context of the Danish fire loss data.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Risk measure estimation under two component mixture models with trimmed data

Bakar

Nadarajah

2018

Journal of Applied Statistics

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“…Using (17) and (18) in (19), we obtain the variance of the EP-W distribution. Furthermore, the mgf of the EP-W distribution, M X (t), is given by…”

Section: Momentsmentioning

confidence: 99%

“…Finite mixture models represent a further approach to define very flexible distributions which are also able to capture, for instance, multimodality of the underlying distribution [18][19][20]. The price to pay for this greater flexibility is a more complicated and computationally challenging inference.…”

Section: Introductionmentioning

confidence: 99%

New methods to define heavy-tailed distributions with applications to insurance data

Ahmad

Mahmoudi

Hamedani

et al. 2020

Journal of Taibah University for Science

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Heavy-tailed distributions play an important role in modelling data in actuarial and financial sciences. In this article, nine new methods are suggested to define new distributions suitable for modelling data with an heavy right tail. For illustrative purposes, a special sub-model is considered in detail. Maximum likelihood estimators of the model parameters are obtained and a Monte Carlo simulation study is carried out to assess the behaviour of the estimators. Furthermore, some actuarial measures are calculated. A simulation study based on these actuarial measures is done. The usefulness of the proposed model is proved empirically by means of two real data sets. Finally, Bayesian analysis and performance of Gibbs sampling for the data sets are also carried out.

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“…if each mixture component corresponds to an underlying subpopulation (for details about merging mixture components, refer to Baudry et al (2010)). Our rationale is also shared, among others, by Miljkovic and Grün (2016), who defined a mixture model for the distribution of insurance losses where the number of components is allowed to vary from 1 to 8, and six families of component distributions, with a different number of parameters, are considered. The 'double' flexibility of our zero-and-one inflated mixture model has implications also on the overall number of parameters, say #par.…”

Section: The Zero-and-one Inflated Mixture Modelmentioning

confidence: 99%

Modelling the Loss Given Default Distribution via a Family of Zero-and-one Inflated Mixture Models

Tomarchio

Punzo

2019

Journal of the Royal Statistical Society Series A: Statistics in Society

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Summary The empirical distribution of the loss given default (LGD) has support [0,1], contains an excess of 0s and 1s, and is often multimodal on (0,1). Though some parametric models have been used in the credit risk literature to model the LGD distribution, these peculiarities call for more flexible approaches. Thus, we introduce a zero‐and‐one inflated mixture where a three‐level multinomial model is considered for the membership of the LGD values to the sets {0}, (0,1) and {1}, whereas a finite mixture of distributions is used on (0,1). To allow for more flexible shapes on (0,1), we consider component distributions already defined on (0,1) and distributions on (−∞,∞) mapped on (0,1) via the inverse logit transformation. This yields a family of 13 zero‐and‐one inflated mixture models. They are applied to two data sets of LGDs on loans: one from a European Bank and the other from the Bank of Italy. The best performers in our family, selected via classical information criteria, are then compared with several well‐established semiparameteric or non‐parametric approaches via a convenient simulation‐based procedure.

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Modeling loss data using mixtures of distributions

Cited by 88 publications

References 20 publications

Risk measure estimation under two component mixture models with trimmed data

Risk measure estimation under two component mixture models with trimmed data

New methods to define heavy-tailed distributions with applications to insurance data

Modelling the Loss Given Default Distribution via a Family of Zero-and-one Inflated Mixture Models

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