Sankhya: The Indian Journal of Statistics

2005, Volume 67, Pt. 1, 106--125

Discrete Life Distributions with Decreasing Reversed Hazard

By

Asok K. Nanda, Indian Institute of Technology, Kharagpur, India
Debasis Sengupta, Indian Statistical Institute, Kolkata, India

SUMMARY. This paper considers the class of discrete distributions for which the distribution function is a log-concave sequence. It is shown that such distributions arise from a wide variety of circumstances in Reliability, and that these have a decreasing reversed hazard rate. After examining the closures of the class under certain key operations, sharp upper and lower bounds on the reliability function for the member distributions are given. Some useful inequalities for maintained systems are provided. Some results for the related class of discrete concave distributions are also given.

AMS (1991) subject classification. Primary 60N05; secondary 90B25.

Key words and phrases. Log-concave distribution, concave distribution, reliability bound, maintained system, shock model.

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