Compound unimodal distributions for insurance losses

Punzo, Antonio; Bagnato, Luca; Maruotti, Antonello

doi:10.1016/j.insmatheco.2017.10.007

Cited by 50 publications

(33 citation statements)

References 36 publications

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“…3 Parameters are estimated via the maximum likelihood (ML) procedure and the whole analysis is made in the R statistical software (R Core Team, 2016). For the models LN, G, W, and L the estimated parameters are obtained by the fitdist() function of the fitdistrplus package (Delignette-Muller et al, 2017), while for the model IG the estimates are obtained using the function provided in Punzo et al (2017) is the same for all the years. The same result holds if the BIC index is considered (for brevity's sake the results are not reported here).…”

Section: Firm Size Distributionmentioning

confidence: 99%

Waiting for Godot: The Failure of SMEs in the Italian Manufacturing Industry to Grow

2018

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All rights reserved. Photocopies for personal use of the reader, not exceeding 15% of each volume, may be made under the payment of a copying fee to the SIAE, in accordance with the provisions of the law n. 633 of 22 april 1941 (art. 68, par. 4 and 5). Reproductions which are not intended for personal use may be only made with the written permission of CLEARedi, Centro Licenze e Autorizzazioni per le Riproduzioni Editoriali,

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Section: Firm Size Distributionmentioning

confidence: 99%

Waiting for Godot: The Failure of SMEs in the Italian Manufacturing Industry to Grow

2018

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“…Another prominent approach is compounding of distributions to cater data modelling with unimodality, right-skewness and heavy tails [8,15,16]. However, the density obtained via this method may not have a closed form expression which makes the estimation more cumbersome as shown in Punzo et al [15]. For a brief review about compounding of distributions, we refer to Tahir and Cordeiro [17].…”

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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“…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 [ 15 ]. The price to pay for this greater flexibility is a more complicated and computationally challenging inference.…”

Section: Introductionmentioning

confidence: 99%

Type-I heavy tailed family with applications in medicine, engineering and insurance

et al. 2020

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In the present study, a new class of heavy tailed distributions using the T-X family approach is introduced. The proposed family is called type-I heavy tailed family. A special model of the proposed class, named Type-I Heavy Tailed Weibull (TI-HTW) model is studied in detail. We adopt the approach of maximum likelihood estimation for estimating its parameters, and assess the maximum likelihood performance based on biases and mean squared errors via a Monte Carlo simulation framework. Actuarial quantities such as value at risk and tail value at risk are derived. A simulation study for these actuarial measures is conducted, proving that the proposed TI-HTW is a heavy-tailed model. Finally, we provide a comparative study to illustrate the proposed method by analyzing three real data sets from different disciplines such as reliability engineering, bio-medical and financial sciences. The analytical results of the new TI-HTW model are compared with the Weibull and some other non-nested distributions. The Baysesian analysis is discussed to measure the model complexity based on the deviance information criterion.

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Compound unimodal distributions for insurance losses

Cited by 50 publications

References 36 publications

Waiting for Godot: The Failure of SMEs in the Italian Manufacturing Industry to Grow

Waiting for Godot: The Failure of SMEs in the Italian Manufacturing Industry to Grow

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

Type-I heavy tailed family with applications in medicine, engineering and insurance

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