title: How to fit data in the form of vectors to Gumbel copula in R?
body: <p>I am relatively new to R. For my final exam at university I decided to write a dissertation on copulas and so I collected some knowledge of the theory behind copulas, what they are and how they work. I also program in R but have never used copulas in R therefore I am a novice to copulas in R.</p>
  
  <p>My question is:
  how can I fit raw data (in the form of an R vector) to a Gumbel copula?</p>
  
  <p>Here is the format of my data:</p>
  
  <pre><code>x &lt;- c(x1,x2,x3,...,xn)
  y &lt;- c(y1,y2,y3,...,yn)
  </code></pre>
  
  <p>Right now I'm using the copula package, I know how to generate random copulas and Gumbel copulas given theta as below:</p>
  
  <pre><code>#independence case
  r_matrix &lt;- t(rgumbel(2000,theta=1))
  plot(r_matrix[1,], r_matrix[2,], col="blue", main="Gumbel, independence case")
  positive dependence
  r_matrix &lt;- t(rgumbel(2000,theta=3))
  plot(r_matrix[1,], r_matrix[2,], col="blue", main="Gumbel, Positive dependence")
  </code></pre>
  
  <p>However I do not know how to estimate theta.. I know what Spearman's Rho and Kendall's Tau are, if that could help.
  Could you please help me to fit x and y to the Gumbel copula? Should I use another package? Thank you</p>