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I want to find the log likelihood of data given Gamma, Weibull and Log normal distributions in R. How do I proceed given that I have already estimated the parameters of the respective distributions?

Ben Bolker
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user3309969
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    Consider posting example data and functional code that estimates the parameters. – Mark Miller Feb 18 '14 at 05:51
  • These links [here](http://stat.ethz.ch/R-manual/R-devel/library/stats4/html/mle.html), [here](http://en.wikibooks.org/wiki/R_Programming/Maximum_Likelihood) and [here](https://r-forge.r-project.org/scm/viewvc.php/*checkout*/paper/CompStat/maxLik.pdf?revision=1114&root=maxlik&pathrev=1114) would be good starting point. – MYaseen208 Feb 18 '14 at 06:28
  • This sound like a request to do your homework, but without the actual question. – IRTFM Feb 18 '14 at 07:49
  • i have done my parameters estimation as follows:fitdistr(x,'Gamma') shape rate 451.76954 202.13089 ( 31.96263) ( 14.30864) fitdistr(x,'Weibull') shape scale 20.618605163 2.285169506 ( 0.696335843) ( 0.005879705) fitdistr(x,'lognormal') meanlog sdlog 0.803152625 0.047006742 (0.002353281) (0.001664021) now i want to find the respective log likelihood @ Mark Miller – user3309969 Feb 18 '14 at 14:19

1 Answers1

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Here's an example for Gamma. Weibull and log-Normal follow exactly the same procedure.

set.seed(101)
x <- rgamma(20,shape=3,rate=2.5)

library(MASS)
(ff <- fitdistr(x,"gamma"))
##     shape       rate  
##   4.452775   4.175653 
##  (1.358630) (1.348722)

fitdistr has a log-likelihood accessor method:

logLik(ff)
## 'log Lik.' -13.14535 (df=2)

Or you can do it by hand:

sum(dgamma(x,shape=coef(ff)["shape"],rate=coef(ff)["rate"],log=TRUE))
## [1] -13.14535

or a little bit of sugar/R-magic:

with(as.list(coef(ff)),
      sum(dgamma(x,shape=shape,rate=rate,log=TRUE)))

For the other distributions

  • densfun="weibull" -> dweibull()
  • densfun="lognormal" -> dlnorm()

In both cases the parameterizations/names of the parameters match between fitdistr and the corresponding density functions.

Ben Bolker
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