In this paper, we investigate the computation of the moments of the compound Poisson sums with discounted claims when introducing dependence between the interclaim time and the subsequent claim size. The dependence structure between the two random variables is defined by a Farlie-Gumbel-Morgenstern copula. Assuming that the claim distribution has finite moments, we give expressions for the firs...

A new G family of probability distributions called the type I quasi Lambert is defined and applied for modeling real lifetime data. Some bivariate families using "Farlie-Gumbel-Morgenstern copula", "modified Farlie-Gumbel-Morgenstern "Clayton copula" "Renyi's entropy are derived. Three characterizations presented. its statistical properties derived studied. The maximum likelihood estimation, pr...

We propose a more flexible symmetric counterpart of the Huang–Kotz’s copula 1st type. Both and type provide same improvement in correlation level. Moreover, proposed includes special cases many other extensions Farlie–Gumbel–Morgenstern (FGM) copula.

Abstract This paper focuses on the parameter estimation for d -variate Farlie–Gumbel–Morgenstern (FGM) copula ( $$d\ge 2$$ d ≥ 2 ), which has $$2^d-d-1$$ - 1 dependence parameters to be estimated;...

We propose a new family of copulas generalizing the Farlie-Gumbel-Morgenstern family and generated by two univariate functions. The main feature of this family is to permit the modeling of high positive dependence. In particular, it is established that the range of the Spearman’s Rho is [−3/4, 1] and that the upper tail dependence coefficient can reach any value in [0, 1]. Necessary and suffici...

the complex system containing n elements, each having three dependent components are described. the reliability and mean residual life of such systems with intact components at time t are investigated using a trivariate binomial model. considering a farlie-gumbel-morgenstern family, some graphical representations are given.