# How do I fit a set of data to Burr Distribution in R?

For example I have a data set as: (2042.044,2218.153,3670.893,5149.684,5533.429,7111.183,11041.569,15459.771,783.477,1701.520,40810.770,67905.857)

How do I fit the above data in Burr distribution to compute its parameters in R? fitdist does not provide Burr distribution. Can I explicitly define my probability distribution function for the required computation?

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A Burr distribution (at least as defined in Wikipedia) will not fit your data. You need a scaled version of this distribution whose CDF $F$ has three positive parameters, $c,k,\sigma$, and is given by $F(x;c,k,\sigma)=1-(1+(x/\sigma)^c)^{k+1}.$ That will fit your data nicely with $\hat c \approx 2.1, \hat k \approx 0.4,$ and $\hat\sigma \approx 2460$. – whuber May 8 '14 at 21:07

Yeah, in ?fitdistr it says you can pass it a density function (CDF), so we just need to define a density function for the Burr distribution. Note that I'm not familiar with the Burr distribution so I just pulled it's CDF off of Wikipedia.

dburr <- function(x, c = 1, k = 1) 1 - (1 + x ^ c) ^ (-k)

# Simulate data from log logistic for a test case
obs <- rllog(100)

library(MASS)
fitdistr(x = obs,
densfun = dburr,
start = list(c = 1, k = 1), # need to provide named list of starting values
lower = list(c = 0, k = 0)) # and named list of lower bounds since c, k > 0


I'm also not sure what the relationship is between Burr and log-logistic, so I don't know what the "right" answer is...

Looking under the CRAN Task View on Distributions, apparently the VGAM package includes the Pareto Type-IV distribution, which includes Burr's distribution somehow. So if you know how to parameterize Pareto-IV to become Burr, you can use their dparetoIV function to for fitdstr, and their rparetoIV if you want to simulate data.

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It seems like the actuar package provides the burr distribution: artax.karlin.mff.cuni.cz/r-help/library/actuar/html/Burr.html – emschorsch Feb 6 '15 at 4:38