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?
Please Help as I am a newbie to R.
 A: 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
library(FAdist)
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.
