Reliability study of proportional odds family of discrete distributions

ABSTRACT

The proportional odds model gives a method of generating new family of distributions by adding a parameter, called tilt parameter, to expand an existing family of distributions. The new family of distributions so obtained is known as Marshall–Olkin family of distributions or Marshall–Olkin extended distributions. In this paper, we consider Marshall–Olkin family of distributions in discrete case with fixed tilt parameter. We study different ageing properties, as well as different stochastic orderings of this family of distributions. All the results of this paper are supported by several examples.

KEYWORDS:

• Marshall–Olkin extended distribution
• stochastic ageing
• stochastic orders

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E15

Acknowledgments

The support received from IISER Kolkata to carry out this research work is gratefully acknowledged by Pradip Kundu.

Funding

The financial support from NBHM, Govt. of India (vide Ref. No. 2/48(25)/2014/NBHM(R.P.)/R&D II/1393 dt. February 3, 2015) is duly acknowledged by Asok K. Nanda.