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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.1 No.1 pp.87-92
DOI :

Statistical Inference for an Arithmetic Process

Leung Kit-Nam Francis†
City University of Hong Kong

Abstract

A stochastic process {An, n = 1,2,...} is an arithmetic process (AP) if there exists some real number, d, so that {An + (n 1)d, n = 1,2,…} is a renewal process (RP). AP is a stochastically monotonic process and can be used for modelling a point process, i.e. point events occurring in a haphazard way in time (or space), especially with a trend. For example, the events may be failures arising from a deteriorating machine; and such a series of failures is distributed haphazardly along a time continuum. In this paper, we discuss estimation procedures for an AP, similar to those for a geometric process (GP) proposed by Lam (1992). Two statistics are suggested for testing whether a given process is an AP. If this is so, we can estimate the parameters d, and of the AP based on the techniques of simple linear regression, where and are the mean and variance of the first random variable A1 respectively. In this paper, the procedures are, for the most part, discussed in reliability terminology. Of course, the methods are valid in any area of application, in which case they should be interpreted accordingly.

 

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