A Numerical Algorithm for Recursively-Defined Convolution Integrals Involving Distribution Functions

Robert Cleroux and Denis J. McConalogue
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Robert Cleroux: University of Montreal
Denis J. McConalogue: University College, Dublin

Management Science, 1976, vol. 22, issue 10, 1138-1146

Abstract: Reliability studies give rise to families of distribution functions F (n) defined recursively by the repeated convolution of a distribution function F with itself according to the scheme 0 t P (s) (t - x)Q (r) (x) dx where P (s) and Q (r) are the sth and rth members of families generated from distribution functions P and Q, not necessarily distinct. It is seldom possible or convenient to express the F (n) in analytical form. An algorithm based on cubic spline interpolation is given here for recursively generating continuous numerical approximations to the F (n) in a form which allows them to be convoluted together to provide useful approximation to the second of the above integrals.

Date: 1976
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