论文信息 - On the estimation of the adjustment coefficient in risk theory via intermediate order statistics

On the estimation of the adjustment coefficient in risk theory via intermediate order statistics

Abstract A sequence of intermediate order statistics is proposed to estimate the adjustment coefficient in risk theory. The underlying r.v.’s may be viewed as maximum waiting times in busy cycles of GI⧸G⧸1 queueing models under light traffic. We prove strong consistency and study also rates of convergence. We give an example, and present simulation studies as well, for illustrating the behaviour of the proposed estimator.

Josef Steinebach | Miklós Csörgő | J. Steinebach | M. Csörgo

[1] A note on positive supermartingales in ruin theory , 1989 .

[2] Lajos Horváth. On the tail behaviour of quantile processes , 1987 .

[3] B. Cooil. Limiting Multivariate Distributions of Intermediate Order Statistics , 1985 .

[4] Lajos Horváth,et al. Estimates for the probability of ruin starting with a large initial reserve , 1986 .

[5] J. Kiefer. Iterated Logarithm Analogues for Sample Quantiles When P n ↓0 , 1985 .

[6] Jef L. Teugels,et al. Empirical Laplace transform and approximation of compound distributions , 1990, Journal of Applied Probability.

[7] Lajos Horváth,et al. Approximation of intermediate quantile processes , 1987 .

[8] U. Herkenrath. On the estimation of the adjustment coefficient in risk theory by means of stochastic approximation procedures , 1986 .

[9] P. Deheuvels. Strong laws for the k-th order statistic when k≦c log2n , 1986 .

[10] V. Mammitzsch. A note on the adjustment coefficient in ruin theory , 1986 .