My bibliography  Save this paper

Local limit theorems for shock models

Author

Listed:
• Omey, Edward

() (Hogeschool-Universiteit Brussel (HUB), Belgium)

• Vesilo, Rein

() (Macquarie University, Dept. of Electronics, Sydney, Australia)

Abstract

In this paper we study the local behaviour of a characteristic of two types of shock models. In many physical systems, a failure occurs when the stress or the fatigue, represented by $\epsilon(n)$, reaches a critical level $x$. We are interested in the time $\tau(x)$ for which this happens for the first time. In the cumulative shock model we assume that $\epsilon(n) = \sum_{i=1}^n X_i$ is an acummulation of independent shocks $\Ksi_i$. In the extreme shock model, we assume that $\epsilon(n) = \max(X_1,X_2, ..., X_n)$ where the damage to the system is measured in terms of the largest shock up to now. For both models we.obtain a local limit theorem for the corresponding time $\tau(x)$.

Suggested Citation

• Omey, Edward & Vesilo, Rein, 2011. "Local limit theorems for shock models," Working Papers 2011/23, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
• Handle: RePEc:hub:wpecon:201123
as

File URL: https://lirias.hubrussel.be/bitstream/123456789/5156/1/11HRP23.pdf

References listed on IDEAS

as
1. Omey, E. & Rachev, S. T., 1991. "Rates of convergence in multivariate extreme value theory," Journal of Multivariate Analysis, Elsevier, vol. 38(1), pages 36-50, July.
Full references (including those not matched with items on IDEAS)

Keywords

Renewal theory; shock models; regular variation; extreme value theory; local limit theory;

NEP fields

This paper has been announced in the following NEP Reports:

Corrections

All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hub:wpecon:201123. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sabine Janssens). General contact details of provider: http://edirc.repec.org/data/emhubbe.html .

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.