A new class of bivariate copulas: dependence measures and properties

Bekrizadeh, Hakim; Jamshidi, Babak

doi:10.1007/s40300-017-0107-1

Cited by 14 publications

(10 citation statements)

References 19 publications

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“…Nevertheless, the Farlie-Gumbel-Morgenstern copula has been shown to be somewhat limited since it does not allow the modeling of high dependencies. Indeed, its dependence parameter is θ ∈ [−1, 1], so its Spearman's rho and Kendall's tau are ρ θ = θ/3 ∈ [−1/3, 1/3] and τ θ = 2θ/9 ∈ [−2/9, 2/9], respectively (see, e.g., [7,8,37] and references therein). This limited range of dependence restricts the usefulness of this copula for modeling.…”

Section: Introductionmentioning

confidence: 99%

The risk model with stochastic premiums, dependence and a threshold dividend strategy

Ragulina¹

2017

Modern Stoch. Theory Appl.

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The paper deals with a generalization of the risk model with stochastic premiums where dependence structures between claim sizes and inter-claim times as well as premium sizes and inter-premium times are modeled by Farlie-Gumbel-Morgenstern copulas. In addition, dividends are paid to its shareholders according to a threshold dividend strategy. We derive integral and integro-differential equations for the Gerber-Shiu function and the expected discounted dividend payments until ruin. Next, we concentrate on the detailed investigation of the model in the case of exponentially distributed claim and premium sizes. In particular, we find explicit formulas for the ruin probability in the model without either dividend payments or dependence as well as for the expected discounted dividend payments in the model without dependence. Finally, numerical illustrations are presented.

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Section: Introductionmentioning

confidence: 99%

The risk model with stochastic premiums, dependence and a threshold dividend strategy

Ragulina¹

2017

Modern Stoch. Theory Appl.

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“…One of the advantages of the generalized FGM copula has wider range of correlation compared to regular FGM copula. According to Bekrizadeh and Jamshidi (2017), the estimated correlations based on the generalized FGM copula is closer to the actual correlation of the observed data compared to FGM copula. This conclusion is also shown in diabetic retinopathy study data.…”

Section: Introductionmentioning

confidence: 84%

“…In this paper, a mixture model is applied to analyze a bivariate censored data with different susceptibilities. A correlation coefficient is applied for cure rates and a generalized bivariate Farlie Gumbel Morgenstern (FGM) copula, proposed by Bekrizadeh and Jamshidi (2017), is applied for the association of bivariate failure times. As studied in Louzada et al (2013), it showed a weak dependence between tow lifetimes in the diabetic retinopathy study data.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Bivariate Cure Rate Models Using Copula Functions

Huang¹,

Zhou²,

Ebrahimi³

2022

IJSP

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Bivariate survival cure rate models extend the understanding of time-to-event data by allowing for a cured fraction of the population and dependence between paired units and make more accurate and informative conclusions. In this paper, we propose a Bayesian bivariate cure rate mode where a correlation coefficient is used for the association between bivariate cure rate fractions and a new generalized Farlie Gumbel Morgenstern (FGM) copula function is applied to model the dependence structure of bivariate survival times. For each marginal survival time, we apply a Weibull distribution, a log normal distribution, and a flexible three-parameter generalized extreme value (GEV) distribution to compare their performance. For the survival model fitting, DIC and LPML are used for model comparison. We perform a goodness-of-fit test for the new copula. Finally, we illustrate the performance of the proposed methods in simulated data and real data via Bayesian paradigm.

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“…To address this issue, Amblard and Girard () proposed another extension, but its application is limited because of a singular component concentrated on the diagonal. Some other extensions of FGM coupla are discussed in Ahn () and Bekrizadeh and Jamshidi (). As mentioned before, it is a challenging problem to develop a bivariate life distribution with the flexibility that the correlation coefficient takes any value in the interval

false[- 1, 0 false]

.…”

Section: Introductionmentioning

confidence: 99%

A bivariate life distribution and notions of negative dependence

Bhuyan

Ghosh

Majumder

et al. 2020

Stat

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Bivariate life distributions used to model negative dependence typically possess certain limitations; in particular, the correlation coefficient takes values in a restricted subrange of . We construct a new bivariate life distribution to remedy this. Properties of the proposed distribution are studied. It is shown that the distribution satisfies most of the popular notions of negative dependence prevalent in the literature. Stress–strength reliability bounds are obtained, and parameter estimation methodology has been discussed. Performance of the estimators are compared through a simulation study.

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A new class of bivariate copulas: dependence measures and properties

Cited by 14 publications

References 19 publications

The risk model with stochastic premiums, dependence and a threshold dividend strategy

The risk model with stochastic premiums, dependence and a threshold dividend strategy

Bayesian Bivariate Cure Rate Models Using Copula Functions

A bivariate life distribution and notions of negative dependence

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