CDF(cumulative distribution function) starts not from 0

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Xiaowei Wang
Xiaowei Wang on 21 Sep 2015
Commented: Xiaowei Wang on 22 Sep 2015
I have a dataset, then i want to know the distribution, i used exppdf(X,mu), but the result is not reasonable, please see the figure, why the CDF(cumulative distribution function) starts not from 0? And the PDF(probability density function) seems too small. How can i solve this problem?
  2 Comments
Greig
Greig on 21 Sep 2015
The reason that the PDF and CDF don't start at zero probability is because the distributions that you specify exist outside of the X values you used.
These two functions generate the theoretical PDFs and CDFs for the specified distributions at the X values you input. They are not for data fitting.
See my answer below for more details.

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Answers (2)

Greig
Greig on 21 Sep 2015
It seems like your choice of parametric distribution is not appropriate for your data and it seems that you might be approaching the problem in the wrong way.
First things first... What are your data? What is their physical meaning? Do they have lower or upper bounds? What do you want to do with the distribution fit? Have previous analyses (by others) justified the use of a exponential or chi-squared distribution? All of these questions will help you to decide what type of distribution is appropriate to fit to your data.
Second things second, fitting... Do you have Statistics Toolbox? If so, then dfittool is a good place to start. In command window type
doc 'Model Data Using the Distribution Fitting App'
and choose the first option.
If you can provide us with more info about your data we can probably help some more.

Xiaowei Wang
Xiaowei Wang on 21 Sep 2015
Thanks for your nice reply. The data i used is uploaded, it is the simulation result, i could find the maximum and minimum (upper and lower)bounds, but no idea why doing this. My purpose is to know which distribution my data fits. Yes, i had Statistics Toolbox and tried with dfitool, there are lots of distributio functions, how to choose the most appropraie one? Is there some parameters as measurand, e.g, the value of the error?
  3 Comments
Xiaowei Wang
Xiaowei Wang on 22 Sep 2015
Hello, Greig,that is correct, directivity is a quantity in electromagnetic theory, which is ratio of U over V. It has a range from 0 to infinity, where i use linear values, not in dB. Then i tried gamma distribution gampdf and gamcdf, still the problem, the values of CDF not starts from 0 (not appropraite). Then next i tried gammafit, but this seems only to obtain some parameters. Finally i used dfittool, and the normal distribution is better approached (in attachment). Although normal distribution is for the whole real line (-infinity, infinity) , nor sure i am correct. I will try the distribution of directivity itself, and also the distribution for U and P themselves, whether or not they are equivalent.

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