Burr distribution | Vose Software

Burr distribution

Format: Burr(a, b, c, d)


The Burr distribution is a right-skewed distribution bounded at the minimum value of a. b is a scale parameter while c and d control its shape. Burr(0,1,c,d) is a unit Burr distribution. Examples of the Burr distribution are given below:


The Burr distribution has a flexible shape and controllable scale and location which makes it appealing to fit to data. It is frequently used to model insurance claim sizes, and is sometimes considered as an alternative to a Normal distribution when data show slight positive skewness.


A Burr(a,b,c,1) is the Loglogistic distribution. The Burr distribution is sometimes known as the Burr Type XII distribution, or the Singh-Maddala distribution.

ModelRisk functions added to Microsoft Excel for the Burr distribution

VoseBurr generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseBurrObject constructs a distribution object for this distribution.

VoseBurrProb returns the probability density or cumulative distribution function for this distribution.

VoseBurrProb10 returns the log10 of the probability density or cumulative distribution function.  

VoseBurrFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution.

VoseBurrFitObject constructs a distribution object of this distribution fitted to data.

VoseBurrFitP returns the parameters of this distribution fitted to data.

Burr distribution equations