Consider the problem of fitting a distribution on a data set and suppose that there are two family of distributions; e.g., normal and Laplace.
How can one determine which one fit better?
What methods are there for this problem and what are their advantages and disadvantages?
I believe the Kolmogorov-Smirnov test might be useful to you: http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test
It is implemented in R as ks.test().
Dear Warren,
Thank you very much for your answer.
It seems that your answer holds when comparing two single distribution.
My problem is comparing two family of distributions, especially when they are not distinct, in the sense that there exists at least one member of the first family which is the limiting distribution of a sequence of members of the second family.
What is your idea in this case?
Best,
To answer the question in the title:
If you are comparing a data set to a single theoretical distribution, then ks.test will work as long as you can specify the cumulative distribution function in R for the distribution. You will have to estimate the parameters of the distribution from the data. You can use method of moments or maximum likelihood estimates for that. I suggest checking out the examples in ?ks.test.
I am not sure I have the knowledge to answer your question in the previous post.
There is a nice article in Wikipedia which describes various possibilities to check goodness-of-fit. Kolmogorov-Smirnov is only one possibility.
http://en.wikipedia.org/wiki/Goodness_of_fit
If you want to perform a Kolmogorov-Smirnov Test to a family of distributions and you need to estimate the parameters the problem changes. In the class of normal distributions this leads to the well-known Lilliefors-correction, see also Lilliefors test which should guide you in this direction.
You could also use information criteria, such as the Akaike Information Criterion. very straight forward: Just fit the two models via ML and compare. The smaller AIC indicates better fit. The only precondition is that you have a ML estimator (least squares is also fine). Take great care to either implement the ML estimator yourself, or use one package. The AIC contains large constants that may vary between implementations.
An R library with a wealth of statistical distributions is VGAM.
- Badges
- Science topic
- Similar topics
- Medicine
- Physiology
- Biosignals
- Biomedical Signal Processing
- Statistical Analysis