Rational reconstruction of frailty-based mortality models by a generalisation of Gompertz’ law of mortality

Willemse, W.J.; Kaas, Rob

doi:10.1016/j.insmatheco.2006.07.003

Cited by 16 publications

(10 citation statements)

References 12 publications

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“…smoking, obese). This is similar to Willemse (2004) who argues that frailty can be modeled as an individual age reduction, we model heterogeneity by adding a heterogeneous component to mortality intensity. If x is driven by a¢ ne dynamics equation (23) leads to survival probabilities by a simple application of theorem 1.…”

Section: Heterogeneitymentioning

confidence: 85%

Affine stochastic mortality

Schrager

2006

Insurance: Mathematics and Economics

159

113

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We propose a new model for stochastic mortality. The model is based on the literature on a¢ ne term structure models. It satis…es three important requirements for application in practice: analytical tractibility, clear interpretation of the factors and compatibility with …nancial option pricing models. We test the model …t using data on Dutch mortality rates. Furthermore, we discuss the speci…cation of a market price of mortality risk and apply the model to the pricing of a Guaranteed Annuity Option and the calculation of required Economic Capital for mortality risk.

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Section: Heterogeneitymentioning

confidence: 85%

Affine stochastic mortality

Schrager

2006

Insurance: Mathematics and Economics

159

113

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“…Extreme value theory indicates that the Gumbel distribution is useful for representing the distribution of maximum values when the underlying sample data are normally or exponentially distributed. The Gumbel distribution has been variously called the log-Weibull distribution, the double exponential distribution and the Laplace distribution, and it is often incorrectly referred to as the Gompertz distribution (Willemse & Kaas 2007). Although the Fréchet distribution is named after Fréchet (1927), who used it to model the distribution of the largest order statistic, it was further developed by Fisher & Tippett (1928) and Gumbel (1954).…”

Section: Introductionmentioning

confidence: 99%

Modeling extreme values for height distributions in Pinus pinaster, Pinus radiata and Eucalyptus globulus stands in northwestern Spain

Gorgoso-Varela¹,

García-Villabrille²,

Alboreca³

2016

iForest

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Methods of estimating extreme height values can be used in forest modeling to improve fits to the marginal distribution of heights in the following bivariate diameter-height models: the SBB Johnson's distribution, the bivariate beta (GDB-2) distribution, the bivariate Logit-Logistic (LL-2) distribution and the power-normal (PN) distribution. Some applications to LiDAR derived data are also possible, e.g., for error calibration. Practical applications in forest management may also be considered, e.g., for pruning. In probability theory and statistics, the generalized extreme value (GEV) distribution, also known as the Fisher-Tippett distribution, is a family of continuous probability distributions that combine the Gumbel, Fréchet and Weibull distributions. This study compared the three distributions for fitting extreme values of tree heights (maximum and minimum heights), which were measured in 185 permanent research plots in Pinus pinaster Ait.

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“…It is also known as the logWeibull distribution and the double exponential distribution which is sometimes also called the Laplace distribution. It is often wrongly called the Gompertz distribution (Willemse and Kaas 2007).…”

Section: Introductionmentioning

confidence: 99%

Use of Gumbel and Weibull functions to model extreme values of diameter distributions in forest stands

Gorgoso-Varela

Alboreca

2014

Annals of Forest Science

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& Context Families of the Gumbel (type I), Fréchet (type II) and Weibull (type III) distributions can be combined in the generalized extreme value (GEV) family of distributions. Maximum and minimum values of diameters in forest stands can be used in forest modelling, mainly to define parameters of the functions used in diameter class models as well as in some practical cases, such as modelling maximum diameters for sawing and processing purposes. & Aims The purpose of this study was to examine and compare two extreme value distribution functions (the Gumbel and the Weibull functions) in modelling the distribution of the minimum and the maximum values of representative sets of tree diameter samples. Both of these functions were applied to the lower and upper values of the diameter distributions of the main forest species in northwest Spain: Quercus robur L., Betula pubescens Ehrh., Pinus radiata D. Don, Pinus pinaster Ait. and Pinus sylvestris L. & Methods Parameters of the Gumbel function were estimated using the mode and the moments of the distributions, and parameters of the Weibull function were estimated using the moments method.& Results In general, the Weibull distribution was the most suitable model for describing the maximum diameters. The mode method of the Gumbel yielded the best results for minimum diameters of birch and Monterrey pine. The Gumbel distribution, fitted by either the mode-or momentsbased methods, proved more suitable than the Weibull distribution for describing the minimum diameters in maritime pine and Scots pine stands. & Conclusion In some cases, better results were obtained with the Gumbel than the Weibull distribution for describing the distribution of extreme diameter values in forest stands in northwest Spain. This is the first example of the application of the Gumbel distribution in forest modelling.

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Rational reconstruction of frailty-based mortality models by a generalisation of Gompertz’ law of mortality

Cited by 16 publications

References 12 publications

Affine stochastic mortality

Affine stochastic mortality

Modeling extreme values for height distributions in Pinus pinaster, Pinus radiata and Eucalyptus globulus stands in northwestern Spain

Use of Gumbel and Weibull functions to model extreme values of diameter distributions in forest stands

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