Multivariate geometric distributions generated by a cumulative damage process
By: by J.D. Esary and A.W. Marshall
Contributors: Marshall, A. W.; Naval Postgraduate School (U.S.)
Publisher: Naval Postgraduate School
Published: 1973
Place of publication: Monterey, California
Language: eng
Number of pages: 34
Subjects: Distribution (Probability theory)
Description: Two (narrow and wide) multivariate geometric analogues of the Marshall-Olkin multivariate exponetial distribution are derived from the following cumulative damage model. A set of devices is exposed to a common damage process. Damage occurs in discrete cycles. On each cycle the amount of damage is an independent observation on a nonnegative random variable. Damages accumulate additively. Each device has its own random breaking threshold. A device fails when the accumulated damage exceeds its threshold. Thresholds are independent of damages, and have a Marshall-Olkin multivariate exponential distribution. The joint distribution of the random numbers of cycles up to and including failure of the devices has the wide multivariate geometric distribution. It has the narrow multivariate geometric distribution if the damage variable is infinitely divisible. (Author)
Notes: Title from cover.

"March 1973"--Cover.

"NPS-55EY73041A"--Cover.

DTIC Identifiers: Bivariate analysis, geometric density functions, exponential density functions.

Author(s) key words: Multivariate geometric distributions, compound Poisson process, multivariate exponential distributions, coherent systems, reliability.

Includes bibliographical references (p. 29)

"Approved for public release; distribution unlimited"--Cover.

Technical report; 1973.

kmc/kmc 9/11/09.