Contribution of the Extreme Term in the Sum of Samples with Regularly Varying Tail
نویسنده
چکیده
For a sequence of random variables (X1, X2, . . . , Xn), n ≥ 1, that are independent and identically distributed with a regularly varying tail with index −α, α ≥ 0, we show that the contribution of the maximum term Mn , max(X1, . . . , Xn) in the sum Sn , X1 + · · · + Xn, as n → ∞, decreases monotonically with α in stochastic ordering sense.
منابع مشابه
Two-site localisation in the Bouchaud trap model with slowly varying traps
We consider the Bouchaud trap model on the integers in the case that the trap distribution has a slowly varying tail at infinity. We prove that the model eventually localises on exactly two sites with overwhelming probability. This is a stronger form of localisation than has previously been established in the literature for the Bouchaud trap model on the integers in the case of regularly varyin...
متن کاملHenrik Hult , Filip Lindskog and Thomas Mikosch : Functional large deviations for multivariate regularly varying random walks
We extend classical results by A.V. Nagaev (1969) on large deviations for sums of iid regularly varying random variables to partial sum processes of iid regularly varying vectors. The results are stated in terms of a heavy-tailed large deviation principle on the space of càdlàg functions. We illustrate how these results can be applied to functionals of the partial sum process, including ruin pr...
متن کاملMultivariate MA(∞) processes with heavy tails and random coefficients
Many interesting processes share the property of multivariate regular variation. This property is equivalent to existence of the tail process introduced by B. Basrak and J. Segers [1] to describe the asymptotic behavior for the extreme values of a regularly varying time series. We apply this theory to multivariate MA(∞) processes with random coefficients.
متن کاملAbstracts for the PhD Course on Extremes in Space and Time, May 27-30 Extremes and sums of regularly varying observa- tions
s for the PhD Course on Extremes in Space and Time, May 27-30 Extremes and sums of regularly varying observations Bojan Basrak (University of Zagreb) In the first part, we show how the dependence structure of extremes in a stationary regularly varying sequence can be described, using the concept of the tail process. This is illustrated on some standard time series models. In the second part, we...
متن کاملAn Alternative Characterization of Hidden Regular Variation in Joint Tail Modeling
In modeling the joint upper tail of a multivariate distribution, a fundamental deficiency of classical extreme value theory is the inability to distinguish between asymptotic independence and exact independence. In this work, we examine multivariate threshold modeling based on the framework of regular variation on cones. Tail dependence is described by an angular measure, which in some cases is...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1801.09887 شماره
صفحات -
تاریخ انتشار 2018