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On a Simple Numerical Method for Computing Stieltjes Integrals in Reliability Theory

Published online by Cambridge University Press:  27 July 2009

T. K. Boehme ,
W. Preuss  and
V. van der Wall
T. K. Boehme
Affiliation:
Department of Mathematics University of California, Santa Barbara, California
W. Preuss
Affiliation:
Department of Mathematics Wismar Technical University, Wismar, GDR
V. van der Wall
Affiliation:
Department of Mathematics Wismar Technical University, Wismar, GDR
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Abstract

A simple method of calculating Stieltjes integrals is proposed. The method is essentially the two-point (trapezoidal) rule from numerical analysis. Two theorems yielding error bounds are given. When error requirements are modest (two or three significant decimal places) the method is fast and inexpensive. Examples are given solving the Renewal equation from reliability theory. A program for an HP-41C hand calculator is given, which solves the renewal equation.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 5 , Issue 1 , January 1991 , pp. 113 - 128
Copyright
Copyright © Cambridge University Press 1991

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