title: Difficulty fitting gamma distribution with R
body: <p>I am attempting to estimate parameters for a gamma distribution fit to ecological density (i.e. biomass per area) data. I have been using the fitdistr() command from the MASS package in R (version 3.0.0 : x86_64-w64-mingw32/x64 (64-bit)). This is a maximum likelihood estimation command for distributional parameters.</p>
  
  <p>The vectors of data are quite large, but summary statistics are as follows:</p>
  
  <blockquote>
    <p>Min. = 0;  1st Qu. = 87.67;  Median = 199.5;  Mean = 1255;  Variance =
    2.79E+07;  3rd Qu. = 385.6;  Max. = 33880</p>
  </blockquote>
  
  <p>The code I am using to run the MLE procedure is:</p>
  
  <pre><code>gdist &lt;- fitdistr(data, dgamma, 
                    start=list(shape=1, scale=1/(mean(data))),lower=c(1,0.1))
  </code></pre>
  
  <p>R is giving me the following error:</p>
  
  <blockquote>
    <p>Error in optim(x = c(6.46791148085828, 4060.54750836902,
    99.6201565968665,  :    non-finite finite-difference value [1]</p>
  </blockquote>
  
  <p>Others who have experienced this type of issue and have turned to stackoverflow for help seem to have found the solution in adding the "lower=" argument to their code, and/or removing zeros. I find that R will provide parameters for a fit if I remove the zero observations, but I was under the impression that gamma distributions covered the range 0 &lt;= x > inf (Forbes et al. 2011. Statistical Distributions)?</p>
  
  <p>Have I gotten the wrong impression regarding the range of the gamma distribution? Or is there some other issue I am missing regarding MLE (in which I am a novice).</p>