To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
Show all languages
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.

Burr distribution

From Wikipedia, the free encyclopedia

Burr Type XII
Probability density function
Burr pdf.svg
Cumulative distribution function
Burr cdf.svg
Mean where Β() is the beta function
Ex. kurtosis where moments (see)

where is the Gamma function and is the Fox H-function.[1]

In probability theory, statistics and econometrics, the Burr Type XII distribution or simply the Burr distribution[2] is a continuous probability distribution for a non-negative random variable. It is also known as the Singh–Maddala distribution[3] and is one of a number of different distributions sometimes called the "generalized log-logistic distribution". It is most commonly used to model household income, see for example: Household income in the U.S. and compare to magenta graph at right.

The Burr (Type XII) distribution has probability density function:[4][5]

and cumulative distribution function:

When c = 1, the Burr distribution becomes the Pareto Type II (Lomax) distribution. When k = 1, the Burr distribution is a special case of the Champernowne distribution, often referred to as the Fisk distribution.[6][7]

The Burr Type XII distribution is a member of a system of continuous distributions introduced by Irving W. Burr (1942), which comprises 12 distributions.[8]

YouTube Encyclopedic

  • 1/1
    1 906
  • Topic 2


See also


  1. ^ Nadarajah, S.; Pogány, T. K.; Saxena, R. K. (2012). "On the characteristic function for Burr distributions". Statistics. 46 (3): 419–428. doi:10.1080/02331888.2010.513442.
  2. ^ Burr, I. W. (1942). "Cumulative frequency functions". Annals of Mathematical Statistics. 13 (2): 215–232. doi:10.1214/aoms/1177731607. JSTOR 2235756.
  3. ^ Singh, S.; Maddala, G. (1976). "A Function for the Size Distribution of Incomes". Econometrica. 44 (5): 963–970. doi:10.2307/1911538. JSTOR 1911538.
  4. ^ Maddala, G. S. (1996) [1983]. Limited-Dependent and Qualitative Variables in Econometrics. Cambridge University Press. ISBN 0-521-33825-5.
  5. ^ Tadikamalla, Pandu R. (1980), "A Look at the Burr and Related Distributions", International Statistical Review, 48 (3): 337–344, doi:10.2307/1402945, JSTOR 1402945
  6. ^ C. Kleiber and S. Kotz (2003). Statistical Size Distributions in Economics and Actuarial Sciences. New York: Wiley. See Sections 7.3 "Champernowne Distribution" and 6.4.1 "Fisk Distribution."
  7. ^ Champernowne, D. G. (1952). "The graduation of income distributions". Econometrica. 20 (4): 591–614. doi:10.2307/1907644. JSTOR 1907644.
  8. ^ See Kleiber and Kotz (2003), Table 2.4, p. 51, "The Burr Distributions."

Further reading

This page was last edited on 13 December 2020, at 01:56
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.