A generalization of the lifetime parts of renewal theory

F.W. Steutel; K. Harn, van

A generalization of the lifetime parts of renewal theory

F.W. Steutel, K. Harn, van

Mathematics and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

Abstract

A characterization is given of the random vectors (X, X’) satisfying the equation X ~ X’ ~ U(X + X’), where U and (X, X’) are independent and U is uniformly distributed on (0, 1). It is shown that the lifetime pairs (age and residual life) in a stationary renewal process satisfy this equation, and a somewhat larger class of vectors with this property is constructed. There are interesting analogues for lattice distributions.

Original language	English
Title of host publication	Advances in the theory and practice of statistics
Editors	N.L. Johnson, N. Balakrishnan
Place of Publication	New York
Publisher	Wiley
Pages	89-105
ISBN (Print)	0-471-15574-8
Publication status	Published - 1997

Cite this

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title = "A generalization of the lifetime parts of renewal theory",

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T1 - A generalization of the lifetime parts of renewal theory

AU - Steutel, F.W.

AU - Harn, van, K.

PY - 1997

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N2 - A characterization is given of the random vectors (X, X’) satisfying the equation X ~ X’ ~ U(X + X’), where U and (X, X’) are independent and U is uniformly distributed on (0, 1). It is shown that the lifetime pairs (age and residual life) in a stationary renewal process satisfy this equation, and a somewhat larger class of vectors with this property is constructed. There are interesting analogues for lattice distributions.

AB - A characterization is given of the random vectors (X, X’) satisfying the equation X ~ X’ ~ U(X + X’), where U and (X, X’) are independent and U is uniformly distributed on (0, 1). It is shown that the lifetime pairs (age and residual life) in a stationary renewal process satisfy this equation, and a somewhat larger class of vectors with this property is constructed. There are interesting analogues for lattice distributions.

M3 - Chapter

SN - 0-471-15574-8

SP - 89

EP - 105

BT - Advances in the theory and practice of statistics

A2 - Johnson, N.L.

A2 - Balakrishnan, N.

PB - Wiley

CY - New York

ER -

A generalization of the lifetime parts of renewal theory

Abstract

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