Asymptotic results on the moments of the ratio of the random sum of squares to the square of the random sum
| dc.creator | Ladoucette, S. A. | |
| dc.date | 2005-05-12 | |
| dc.date.accessioned | 2026-07-07T08:06:53Z | |
| dc.date.available | 2026-07-07T08:06:53Z | |
| dc.description | Let \{X_1, X_2, ...\} be a sequence of positive independent and identically distributed random variables of Pareto-type with index α>0 and let \{N(t); t\geq 0\} be a mixed Poisson process independent of the X_i's. For t\geq 0, define T_{N(t)}:=\frac{X_1^2 + X_2^2 + ... + X_{N(t)}^2} {(X_1 + X_2 + ... + X_{N(t)})^2} if N(t)\geq 1 and T_{N(t)}:=0 otherwise. We derive the limiting behavior of the k-th moment of T_{N(t)}, k\in\mathbb{N}, by using the theory of functions of regular variation and an integral representation for \mathbb{E}\{T_{N(t)}^k\}. We also point out the connection between T_{N(t)} and the sample coefficient of variation which is a popular risk measure in practical applications. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0505265 | |
| dc.identifier | http://arxiv.org/abs/math/0505265 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130762 | |
| dc.subject | Probability | |
| dc.subject | Statistics Theory | |
| dc.subject | 60F05 | |
| dc.title | Asymptotic results on the moments of the ratio of the random sum of squares to the square of the random sum | |
| dc.type | text |