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Rational Polynomial Hazard Functions

Volume 6, Number 1, January 2010 - Paper  3 - pp. 35-52

M. BEBBINGTON1, C. D. LAI1, D. N.P. MURTHY2 and R. ZITIKIS3

1Institute of Fundamental Sciences - Statistics, Massey University, Private Bag 11222, Palmerston North New Zealand
2Division of Mechanical Engineering, University of Queensland, Q 4072, Australia
3Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario N6A 5B7, Canada

(Received on February 10, 2009, revised on June 5, 2009)


Abstract:

Lifetime modeling of physical systems and biological organisms involves the use of failure distribution functions. The shape of the hazard rate (HR) function associated with the distribution function characterizes the effect of age (and other factors) on the failure. Examples of failure (and survival) data indicate that the shapes are many and varied, due to many underlying reasons. In this paper we investigate a model where the HR function is a rational function, which is by definition the ratio of two polynomials. The different possible shapes (increasing, decreasing, bathtub, inverted bathtub, modified bathtub, roller-coaster, etc.) of the HR rational functions are identified, and necessary and sufficient conditions on the parameters to ensure their existence are derived.

 

References: 16

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