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In this paper we present two large deviation results for weighted compound sums ∑Ni = 1 ai Xi, where Xi’s are i.i.d. (possibly lattice) random variables, ai’s are non-negative real numbers, and N is a Poisson variable. These results are generalizations of approximations for non-weighted compound sums and for non-compound weighted sums.
Czasopismo
Rocznik
Tom
Strony
357--368
Opis fizyczny
Bibliogr. 13 poz.
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autor
- IGN/COGIT, 2-4 avenue Pasteur, F-94165 Saint-Mandé Cedex, France
Bibliografia
- [1] K. K. Aase, Accumulated claims and collective risk in assurance: Higher order asymptotic approximations, Scand. Actuar. J. (1985), pp. 65-85.
- [2] O. Bonin, Large deviation theorems for weighted sums applied to a geographical problem, J. Appl. Probab. 39 (2) (2002), pp. 251-260.
- [3] S. A. Book, Large deviation probabilities for weighted sums, Ann. Math. Statist. 43 (4) (1972), pp. 1221-1234.
- [4] H. E. Daniels, Saddlepoint approximation in statistics, Ann. Math. Statist. 25 (1954), pp. 631-650.
- [5] P. Embrechts, J. L. Jensen, M. Maejima, and J. L. Teugels, Approximations for compound Poisson and Polyà processes, Adv. in Appl. Probab. 17 (1985), pp. 623-637.
- [6] F. Esscher, On the probability function in the collective theory of risk, Skand. Akt. Tidskr. (1932), pp. 78-86.
- [7] W. Feller, An Introduction to Probability Theory and Its Applications, Vol. II, Wiley, 1970.
- [8] T. Höglund, A unified formulation of the central limit theorem for small and large deviations from the mean, Z. Wahrscheinlichkeitstheorie verw. Gebiete 49 (1979), pp. 105-117.
- [9] J. L. Jensen, Uniform saddlepoint approximations, Adv. in Appl. Probab. 20 (1988), pp. 622-634.
- [10] J. L. Jensen, Saddlepoint Approximations, Clarendon Press, Oxford 1995.
- [11] J. E. Kolassa, Series Approximation Methods in Statistics, Lecture Notes in Statist., Springer, 1997.
- [12] V. V. Petrov, Limit Theorems of Probability Theory: Sequences of Independent Random Variables, Clarendon Press, Oxford 1995.
- [13] G. E. Willmot, The total claims distribution under inflationary conditions, Scand. Actuar. J. (1989), pp. 1-12.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-42da08de-b3fd-43cf-bd42-ef9277964497