Let X 1 ; X 2 ; : : : ; be a sequence of i.i.d. random variables. X j ; j 6 n is called a near-maximum i X j falls within a distance of the maximum M n = max{X 1 ; : : : ; X n }. In this paper, we focus on medium tailed distributions. A useful relationship on the number of near-maxima is built betwe
Limit laws for the number of near maxima via the Poisson approximation
โ Scribed by Anthony G. Pakes; Yun Li
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 311 KB
- Volume
- 40
- Category
- Article
- ISSN
- 0167-7152
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We present a Poisson approximation with applications to extreme value theory. Let X1; X2; : : : be i.i.d. and let n be the j largest order statistics. Then the asymptotic behavior of the vector (M (1) n ; : : : ; M ( j) n ) is the same as that of (M (1) N ; : : : ; M ( j) N ) where N is a random va
Upper and lower bounds are given for the bchaviour of the Poisson-Boltrmann potential of a highly charged, cylindrical polyelectrolyte in exess salt solution as the salt concentration or cylinder radius tends to zero. The exact singular behaviour of the potential very close to the cylinder is given
In this paper, the weakly nonlinear limit for the relaxation approximation of conservation laws in several space dimensions is derived through asymptotic expansions and justified by employing the energy estimates. Compared with the work of G. Q. Chen, C. D. Levermore, and T. P. Liu (1994, Comm. Pure
In this paper we give an extension of the convergence theorem for martingales which are bounded in L, norm. This theorem is used to obtain the law of large numbers under dependent assumptions.