Burr Distribution

In probability theory, statistics and econometrics, the Burr Type XII distribution or simply the Burr distribution is a continuous probability distribution for a non-negative random variable. It is also known as the Singh–Maddala distribution 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:

:
\begin
f(x;c,k) & = ck\frac \\ ptf(x;c,k,\lambda) & = \frac \left( \frac \right)^ \left + \left(\frac\right)^c\right
\end

and cumulative distribution function:

:$F(x;c,k) = 1-\left(1+x^c\right)^$
:F(x;c,k,\lambda) = 1 - \left + \left(\frac\right)^c \right

Related distributions

* When ''c'' = 1, the Burr distribution becomes the Pareto Type II (Lomax) distribution.

* When ''k'' = 1, the Burr distribution is a log-logistic distribution sometimes referred to as the Fisk distribution, a special case of the Champernowne distribution.

* The Burr Type XII distribution is a member of a system of continuous distributions introduced by Irving W. Burr (1942), which comprises 12 distributions.See Kleiber and Kotz (2003), Table 2.4, p. 51, "The Burr Distributions."

* The Dagum distribution, also known as the inverse Burr distribution, is the distribution of 1 / ''X'', where ''X'' has the Burr distribution

References

Further reading

*

{{DEFAULTSORT:Burr Distribution
Continuous distributions