Standard Article


  1. Abba M. Krieger

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a15169

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Krieger, A. M. 2005. Unimodality. Encyclopedia of Biostatistics. 8.

Author Information

  1. University of Pennsylvania, Philadelphia, PA, USA

Publication History

  1. Published Online: 15 JUL 2005


This entry considers the restriction that the density is unimodal on two related problems. The first problem is to obtain refined bounds on the probability in the tail through extensions of Chebyshev's inequality. The second problem is to refine interpolation of distribution functions by obtaining tighter bounds.


  • unimodal densities;
  • Chebyshev's inequality;
  • interpolation