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 distribution has probability density function:
and cumulative distribution function:
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.
The Burr Type XII distribution is a member of a system of continuous distributions introduced by Irving W. Burr, which comprises 12 distributions.
