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Some Ageing Properties of Marshall-Olkin Extended Distribution

Asok K. Nanda, Suchismita Das

Abstract


Marshall and Olkin (1997) [Biometrika, 84, pp. 641-652] have discussed a general method of introducing a parameter, called tilt parameter, to give more flexibility in modeling. In this paper, we take the tilt parameter as a random variable and study its properties for different ageing classes. It is noted that although some ageing classes are closed under this transformation for a fixed tilt parameter family, they are not closed when the tilt parameter is random. We also give upper and lower bounds to the residual survival function as well as of the failure rate function of the transformed model.


Keywords


closure property, positive ageing, negative ageing.

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