A new class of copulas involving geometric distribution: Estimation and applications

A generalized bivariate lifetime distribution based on parallel-series structures

“…It is known that one of the effective ways for evaluating the behaviour of dependent models is to simulate random data from their corresponding copula. Zhang et al [29] presented an algorithm to generate random data from U = max{X 1,1 , . .…”

“…Kundu and Gupta [15] studied this model when the bivariate random vectors have a bivariate Weibull distribution. Furthermore, Zhang et al [29] used this method to construct a new class of dependent models involving geometric distribution. Roozegar and Nadarajah [26] used a similar method for the component-wise maximum (minimum) of the first component and the component-wise minimum (maximum) for the second component of N independent and identical bivariate random vectors by taking N as a power series random variable.…”

Insurance Applications of Some New Dependence Models Derived from Multivariate Collective Models

“…In this contribution we investigate first the basic distributional and extremal properties of F for general Λ. As it will be shown in Section 3, interestingly the extremal properties of F are similar to those of G. With some motivation from Zhang et al (2016), which investigates Model A and its applications, in this paper, we shall discuss parameter estimation and Monte Carlo simulations for parametric families of bivariate df's induced by F . In particular, we apply our results to actuarial modelling of concrete data sets from actuarial literature.…”

“…As discussed in Nelsen (1999), copulas are a popular multivariate distribution when modelling the dependency between insurance risks as they separate the marginals from the dependence structure, see Embrechts (2009), Genest et al (2009) and references therein. With motivation from Zhang and Lin (2016), in this contribution we propose a flexible family of copulas derived from the joint distribution of the largest claim sizes of two insurance portfolios. Next, in order to introduce our model, we consider the classical collective model over a fixed time period of two insurance portfolios with (X i , Y i ) modelling the ith claim sizes of both portfolios and N the total number of such claims.…”

“…The copula C θ of Model A and Model B include the corresponding original copula Q. In particular, if θ = 1 the pdf c θ in (24) becomes the pdf of the original copula Q, see e.g.,Zhang and Lin (2016), while the copula C θ of Model B reduces to the original copula Q when θ = 0.…”