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HandWiki. Uniform Distribution (Continuous). Encyclopedia. Available online: https://encyclopedia.pub/entry/29679 (accessed on 10 October 2026).
HandWiki. Uniform Distribution (Continuous). Encyclopedia. Available at: https://encyclopedia.pub/entry/29679. Accessed October 10, 2026.
HandWiki. "Uniform Distribution (Continuous)" Encyclopedia, https://encyclopedia.pub/entry/29679 (accessed October 10, 2026).
HandWiki. (2022, October 17). Uniform Distribution (Continuous). In Encyclopedia. https://encyclopedia.pub/entry/29679
HandWiki. "Uniform Distribution (Continuous)." Encyclopedia. Web. 17 October, 2022.
Uniform Distribution (Continuous)
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The content is sourced from: https://handwiki.org/wiki/Uniform_distribution_(continuous)

In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions. The distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. The bounds are defined by the parameters, a and b, which are the minimum and maximum values. The interval can be either be closed (eg. [a, b]) or open (eg. (a, b)). Therefore, the distribution is often abbreviated U (a, b), where U stands for uniform distribution. The difference between the bounds defines the interval length; all intervals of the same length on the distribution's support are equally probable. It is the maximum entropy probability distribution for a random variable X under no constraint other than that it is contained in the distribution's support.

rectangular distribution probability theory probability distribution

References

  1. "Uniform Distribution (Continuous)". 2019. https://www.mathworks.com/help/stats/uniform-distribution-continuous.html. 
  2. Illowsky, Barbara (2013). Introductory Statistics. Rice University, Houston, Texas, USA: OpenStax College. pp. 296–304. ISBN 978-1-938168-20-8. https://archive.org/details/IntroductoryStatistics_201904. 
  3. Casella & Berger 2001, p. 626
  4. https://www.stat.washington.edu/~nehemyl/files/UW_MATH-STAT395_moment-functions.pdf
  5. https://galton.uchicago.edu/~wichura/Stat304/Handouts/L18.cumulants.pdf
  6. Nechval KN, Nechval NA, Vasermanis EK, Makeev VY (2002) Constructing shortest-length confidence intervals. Transport and Telecommunication 3 (1) 95-103 https://www.researchgate.net/profile/Konstantin_Nechval/publication/267986471_CONSTRUCTING_SHORTEST-LENGTH_CONFIDENCE_INTERVALS/links/55c37b3008aeb97567400f29.pdf
  7. Walpole, Ronald (2012). Probability & Statistics for Engineers and Scientists. Boston, USA: Prentice Hall. pp. 171–172. ISBN 978-0-321-62911-1. 
  8. Dekking, Michel (2005). A modern introduction to probability and statistics : understanding why and how. London, UK: Springer. pp. 60–61. ISBN 978-1-85233-896-1. https://archive.org/details/modernintroducti00fmde. 
  9. Wanke, Peter (2008). "The uniform distribution as a first practical approach to new product inventory management". International Journal of Production Economics 114 (2): 811–819. doi:10.1016/j.ijpe.2008.04.004. https://www.researchgate.net/publication/223280031. 
  10. Bellhouse, David (May 2005). "Decoding Cardano's Liber de Ludo". Historia Mathematica 32: 180–202. doi:10.1016/j.hm.2004.04.001.  https://dx.doi.org/10.1016%2Fj.hm.2004.04.001
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