Approximation of the Bivariate Renewal Function

Recently, Kambo and his co-researchers (2012) proposed a method of approximation for evaluating the one-dimensional renewal function based on the first three moments. Their method is simple and elegant, which gives exact values for well-known distributions. In this article, we propose an analogous m...

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Bibliographic Details
Published in:Communications in statistics. Simulation and computation 2015-01, Vol.44 (1), p.154-167
Main Authors: Arunachalam, Viswanathan, Calvache, Álvaro
Format: Article
Language:English
Subjects:
Approximation
Bivariate Laplace transform
Bivariate renewal process
Computer simulation
Free replacement warranty
Laplace transforms
Mathematical analysis
Mathematical models
Pareto optimality
Primary 60K05
Secondary 60K20
Two dimensional
Two-dimensional renewal function
Warranties
Weibull distribution
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Summary:Recently, Kambo and his co-researchers (2012) proposed a method of approximation for evaluating the one-dimensional renewal function based on the first three moments. Their method is simple and elegant, which gives exact values for well-known distributions. In this article, we propose an analogous method for the evaluation of bivariate renewal function based on the first two moments of the variables and their joint moment. The proposed method yields exact results for certain widely used bivariate distributions like bivariate exponential distribution, bivariate Weibull distributions, and bivariate Pareto distributions. An illustrative example in the form of a two-dimensional warranty problem is considered and comparisons of our method are made with the results of other models.
ISSN:0361-0918
1532-4141
DOI:10.1080/03610918.2013.770306