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Hazard Rate Function

  1. Satyanshu Kumar Upadhyay

Published Online: 15 JUN 2010

DOI: 10.1002/9780470400531.eorms0371

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Upadhyay, S. K. 2010. Hazard Rate Function. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. Banaras Hindu University, Department of Statistics, DST Centre for Interdisciplinary Mathematical Sciences, Varanasi, India

Publication History

  1. Published Online: 15 JUN 2010


Hazard rate function is an important concept for researchers and practitioners working in areas such as engineering statistics, and biomedical sciences. Hazard rate in fact provides an alternative characterization for the distribution of a random variable, especially when dealing with the lifetime data and it is quite useful in defining and formulating a model. The present article begins with a discussion on how the notion of hazard rate function enters into lifetime data analysis, and provides the general concept and definition of the hazard function for both continuous and discrete variates. The article finally focuses on a few typical shapes of the hazard rate function and comments briefly on some important models that can be useful for the considered shapes. Additional list of references is provided at the end for supplemental reading.


  • lifetime data;
  • hazard rate function;
  • survival function;
  • probability density and mass functions;
  • cumulative hazard;
  • increasing hazard rate;
  • decreasing hazard rate;
  • constant hazard rate;
  • bathtub-shaped hazard rate