Burr distribution
Probability density function
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Cumulative distribution function
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Parameters | |
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Support | |
CDF | |
Mean | where Β() is the beta function |
Median | |
Mode | |
Variance | |
Skewness | |
Ex. kurtosis | where moments (see) |
In probability theory, statistics and econometrics, the Burr Type XII distribution or simply the Burr distribution[1] is a continuous probability distribution for a non-negative random variable. It is also known as the Singh–Maddala distribution[2] 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: Household income in the U.S. and compare to magenta graph at right).
The Burr (Type XII) distribution has probability density function:[3][4]
and cumulative distribution function:
Note when c=1, the Burr distribution becomes the Pareto Type II distribution. When k=1, the Burr distribution is a special case of the Champernowne distribution, often referred to as the Fisk distribution.[5][6]
The Burr Type XII distribution is a member of a system of continuous distributions introduced by Irving W. Burr (1942), which comprises 12 distributions.[7]
See also
- Dagum distribution, also known as the inverse Burr Distribution.
References
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- ↑ Lua error in package.lua at line 80: module 'strict' not found. See Sections 7.3 "Champernowne Distribution" and 6.4.1 "Fisk Distribution."
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- ↑ See Kleiber and Kotz (2003), Table 2.4, p. 51, "The Burr Distributions."
Further reading
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