World Library  
Flag as Inappropriate
Email this Article

Notation in probability

Article Id: WHEBN0015640179
Reproduction Date:

Title: Notation in probability  
Author: World Heritage Encyclopedia
Language: English
Subject: Probability theory, Mathematical notation
Publisher: World Heritage Encyclopedia

Notation in probability

Probability theory and statistics have some commonly used conventions, in addition to standard mathematical notation and mathematical symbols.

Probability theory


  • Greek letters (e.g. θ, β) are commonly used to denote unknown parameters (population parameters).
  • An estimate of a parameter is often denoted by placing a caret or "hat" over the corresponding symbol, e.g. \hat{\theta}, pronounced "theta hat".
  • The arithmetic mean of a series of values x1, x2, ..., xn is often denoted by placing an "overbar" over the symbol, e.g. \bar{x}, pronounced "x bar".
  • Some commonly used symbols for sample statistics are given below:
  • Some commonly used symbols for population parameters are given below:
    • the population mean μ,
    • the population variance σ2,
    • the population standard deviation σ,
    • the population correlation ρ,
    • the population cumulants κr.

Critical values

The α-level upper critical value of a probability distribution is the value exceeded with probability α, that is, the value xα such that F(xα) = 1 − α where F is the cumulative distribution function. There are standard notations for the upper critical values of some commonly used distributions in statistics:

Linear algebra

  • Matrices are usually denoted by boldface capital letters, e.g. A.
  • Column vectors are usually denoted by boldface lower case letters, e.g. x.
  • The transpose operator is denoted by either a superscript T (e.g. AT) or a prime symbol (e.g. A′).
  • A row vector is written as the transpose of a column vector, e.g. xT or x′.


Common abbreviations include:

See also


External links

  • Earliest Uses of Symbols in Probability and Statistics, maintained by Jeff Miller.
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.