3


I'm trying to figure out the usage of the $\chi^2$ distribution. In other words, in what kind of situations it occurs and how is it useful in that situations.
I read the wikipedia definition of $\chi^2$. Can someone give an example of a $\chi^2$ distribution so that I can better understand it?

kjetil b halvorsen
  • 77,844
Can't Tell
  • 581
  • 2
    @Can't Tell: I think there is no rationale behind the chi-square distribution. You can see it as a sum of N(0,1)^2. You can also characterise it via its pdf. The reason why it is introduced is that important test statistics follow that distribution, at least approximately. For instance, the likelihood ratio. – ocram Mar 13 '11 at 13:21
  • @Marco: Thanks for your comment. But I'm not very good with statistics and I don't understand what you mean by sum of N(0,1)^2 or "likelihood ratio". What I was looking for was something like "if you take the case X, the variables Y and Z are independent standard normal random variables and if you plot the values A and B, then that would be a Chi Square distribution." Is such an example possible(with X,Y,Z,A and B)? – Can't Tell Mar 13 '11 at 13:27
  • 2
    @Can't Tell. I am not sure to get what you exactly want. But take two independent standard normal random variables. Square them and add them. This results in a chi-square random variable whose parameter is 2. If you had had 3 normal variables, the parameter would have been 3, etc. – ocram Mar 13 '11 at 13:34
  • 1
    @Can't What does it mean to "understand" a distribution? As it stands, this question seems rather personal and idiosyncratic in that regard. Could you rephrase it so that it might be meaningful to other people? – whuber Mar 14 '11 at 04:50
  • @whuber: I edited the question. Do you think it is okay now? – Can't Tell Mar 14 '11 at 06:55
  • @Can't Much better! I hope it brings in helpful replies. – whuber Mar 14 '11 at 14:55

1 Answers1

2

I found this video useful in finding the solution to my question.

Can't Tell
  • 581